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All Powers start out giving you an initial selection of options. After you meet certain prerequisites other options will become available. For example you won't be offered Focus Fire to deal more Flame damage to bosses until after you have chosen a skill that deals Flame damage.

Legendary Powers require certain prerequisites. That I discuss in the Legendary section at the bottom.

Astral Dark

Initial Offerings

Cloak of Shadow

Special or Tool grants Dark Shell for 1.8s / 2.4s / 3.2s, dealing 10 / 25 / 40 Dark damage and applying 1 stack of Darkness to neaby enemies

Nightfall

Final Strike applies 1 stack of Darkness for 3 / 4 / 5s and deals 10 / 15 / 25 Dark damage.

Secondary Offerings

Call of the Void

Deal 10 / 15 / 20 Dark damage and pull in nearby enemies upon defeating an enemy affected by Darkness.

Core Collapse

Stun nearby enemies for 0.5s / 1s / 1.5s upon defeating an enemy affected by Darkness

Dark Attakcs

+25% / 40% / 60% Attack damage against enemies affected by Darkness.

Dark Embrace

+3% / 4% / 5% damage dealt and +5% / 7% / 10% Move Speed for each Astral Dark power obtained.

Dark Star

Remove all of your Splinter's Revives. Gain +20% damage, plus 40% damage and heal 15% of Max HP for each Splinter's Revive removed.

This power only has one level and cannot be upgraded.

Dragon's Claw

+10% increased damage dealt. Gain an additional 15% / 20% / 25% whenever you select Dragon Coins in the Room Rewards screen.

Eternal Darkness

+50% / 80% / 100% duration of Negative Effects you apply to enemies.

Gift of the Dragon

Gain 120 Dragon coins and 200 Scrap.

This power only has one level and cannot be upgraded.

Lingering Darkness

Darkness deals 10 / 15 / 25 Dark damage per second to affected enemies.

Shifting Shadow

Dash deals 15 / 25 / 35 Dark damage, increased by 300% to targets affected by Darkness.

After Darkness and Flame Damage

*DARK FLAME* (Dark & Flame)

+40% Flame Damage against targets affected by Darkness.

After Darkness and Any Ninja Power???

*FINISHER* (Astral Dark & Ninja)

Attacks and Specials instantly defeat enemies that are below 15% health.

Astral Light

Initial Offerings

Light Attacks

Attack damage increased by 4% / 7% / 10% of Max Health.

Shimmering Shield

Grant Light Shell for 1.5s / 2.5s / 3.5s at the start of your Dash.

Secondary Offerings

Ancestral Guardian

Light Shell increases Elemental damage by 20% / 30% / 40% while active.

Daybreak

Attacks apply 1 / 2 / 3 stack(s) of Blinding Light for 3s / 4s / 5s. Each stack reduces damage dealt by 4% / 6% / 8%. Max 5 Stacks.

Eternal Light

+40% / 60% / 80% Positive Effect duration.

Light Embrace

Reduce damage received by 2% / 2.5% / 3% for each Astral Light power obtained.

Radiant Warrior

Special and Tool grants Light Shell for 1.5s / 3s / 4.5s

Revival

Gain 1 Splinter's Revive(s). +30 / 60 Max Health.

This power can be offered at level 2 but cannot be upgraded.

After Shimmering Shield

Astral Insight

Increase damage by 30% / 40% / 60% while Light Shell is active.

Illumination

Light Shell reflects projectiles. Reflected projectiles deal 45% / 60% / 75% of your Max Health as Light damage.

After Daybreak

Revved Up

Gain +20% / 25% / 30% chance of dodging enemy attacks when they are affected by Blinding Light.

After Light Attacks and Water Damage

*BRIGHT SPRING* (Water & Light)

Attacks restore 2 health.

After Light Attacks and Utrom Damage

*LIGHT HAMMER* (Utrom & Light)

Utrom damage is increased by 10% of your Max Health.

Flame

Initial Offerings

Flame Abilities

Special and Tool deals 15 / 25 / 40 Flame damage.

Flame Dash

Deal 30 / 50 / 70 Flame damage to nearby enemies at the start of a Dash.

Flame Strike

Final Strike causes an explosion, dealing 25 / 35 / 45 Flame damage to nearby enemies.

Furious Attacks

+20% / 35% / 50% Attack Critical Hit chance.

Rage

Deal 40% / 70% / 100% increased damage while below 50% Health.

Rapid Fire

+20% / 35% / 50% damage dealt and +25% / 40% / 55% Move Speed for 25s /35s / 45s after the start of combat.

After Dealing Flame damage

Focus Fire

+15% / 20% / 30% Flame damage against Bosses.

Inferno

Apply Inferno to enemies hit by Flame damage for 3s. Inferno deals 15 / 20 / 25 Flame damage per second.

After Furious Attacks

Precision

+60% / 120% / 180% Critical Hit damage.

Incendiary Strikes

Deal 50 / 75 / 100 Flame damage when scoring a Critical Hit.

After Inferno

Blazing Inferno

+3s / 4s / 5s Inferno duration.

Preheated

+15% / 30% / 60% Global Critical Hit chance against targets affected by Inferno.

After Rapid Fire

Trailblazer

+15s duration of Rapid Fire. Whilst Rapid Fire is active defeating an enemy grants +1 / 2 / 3s duration and +5 / 10 / 15% damage.

After Charge and Fire Damage

*CRITICAL FLOW* (FLAME & Robotics)

Whenever your Charge Effect activates, gain 3% Critical Hit Chance for this room.

After Flame Damage and Darkness

*DARK FLAME* (Dark & Flame)

+40% Flame Damage against targets affected by Darkness.

After Flame Damage and Frost

*FROSTFIRE* (Flame & Water)

Dealing Flame or Water damage with your Attack, Special, or Tool deals 30% damage of the opposite element.

After Flame Damage and applying Ooze

*SPONTANEOUS COMBUSTION* (Flame & Ooze)

Gain a 30% chance to deal 100 Flame damage when applying Ooze.

After Furious Attacks and Shurikens

*TEMPERED SHURIKEN* (Ninja & Flame)

+40% Critical Hit chance with Shuriken.

Ninja

Initial Offerings

Adrenaline

Gain a stack of Adrenaline upon defeating an enemy. Adrenaline increases Physical damage by 5% / 10% / 15%. 5 stacks max.

First Strike

+30% / 45% / 60% damage dealt for 1s after a Dash.

Quick Feet

+1 Dash charge(s).

This power only has one level and cannot be upgraded.

Shinobi Supremacy

+10% / 15% / 20% Dodge chance.

Shuriken Attacks

Attacks have a 30% / 60% / 100% chance to throw a Shuriken forward.

After Adrenaline

Art of Darkness

Adrenaline now also increases Elemental damage by 15% / 20% / 25%.

Heightened Senses

Gain 1 / 2 / 3 stack(s) of Adrenaline upon a Final Strike.

After Shuriken Attacks or any Shuriken Tool

Quick Hands

+1 / 2 / 3 Shuriken thrown.

Shuriken Breaker

Shuriken apply Guard Break to enemy targets for 2s. Guard Break increases damage received by 15% / 25% / 35%.

Shuriken Engineer

Shuriken have a 30% / 60% / 100% chance of triggering Tool bonuses.

Throwing Mastery

+40% / 65% / 90% Shuriken damage.

Throwing Arts: Chakram*

Shuriken now boomerang, returning to your current position. -30% / -5% / 20% Shuriken Damage.

Throwing Arts: Ricochet*

Shuriken now ricohet, bouncing off of enemies. -20% / +10% / +40% Shuriken damage.

*Choosing Chakram or Ricochet will make the other stop appearing.

After Shinobi Supremacy

Ninjutsu Tactics

+15% / 25% / 25% Global Critical Hit chance for 2s / 2.5s / 3s upon Dodge.

After Shuriken Attacks or any Shuriken Tool,
and Ricochet or Chakram,
and Quick Feet or First Strike

Extended Assault

Throw 1 / 2 / 3 Shuriken forward at the start of your Dash.

After Any Ninja Power?? and Darkness

*FINISHER* (Astral Dark & Ninja)

Attacks and Specials instantly defeat enemies that are below 15% health.

After Quick Feet and Dealing Utrom damage

*REVOLUTION* (Utrom & Ninja)

Dash Attack's damage is increased by 1% of the enemies' Max Health.

After Adrenaline and applying Ooze

*SLIPPERY* (Ooze & Ninja)

Gain 20% Move Speed and charge Tool and Special 100% faster while at maximum Adrenaline.

After Shurikens and Furious Attacks

*TEMPERED SHURIKEN* (Flame & Ninja)

+40% Critical Hit chance with Shuriken.

Ooze

Initial Offerings

Ooze Abilities

Special and Tool applies 1 / 2 / 3 stack(s) of Ooze.

Ooze Attack

Attacks hace a 25% / 33% / 50% chance to apply 1 stack of Ooze.

Ooze Dash

Apply 1 / 2 / 3 stack(s) of Ooze to enemies hit by your Dash.

Ooze Strike

Final Strike applies 2 / 4 / 6 stack(s) of Ooze.

Shelf Life

Boosts last for an additional 4 / 5 / 6 rooms.

Special Spice

50% / 75% / 100% increased effectiveness of Boosts.

After applying Ooze

Catalytic Consequence

Deal +15 / 25 / 35 damage with your Dash Attack for each Stack of Ooze on the enemy.

Chunky Mixture

Ooze can now stack up to 6 / 8 / 10 time(s).

Goo

+60% / +120% / +180% Ooze damage per second.

Goo'dbye

Enemies affected by Ooze now explode on defeat, dealing 50 / 100 / 150 Ooze damage to nearby enemies.

Living Ingredients

When Ooze expires, it is reapplied to 1 / 2 / 3 nearby unaffected enemies.

Potency

Ooze is now applied with an additional 1 / 2 / 3 stack(s).

Unfortunate Odor

Deal 10 / 45 / 80 Ooze damage and Stun enemies for 1s when applying Ooze. Bosses are not stunned.

After applying Ooze and Utrom Damage.

*SECRET OF THE OOZE* (Utrom & Ooze)

Reduce damage received by 30%

After applying Ooze and Adrenaline

*SLIPPERY* (Ninja & Ooze)

Gain 20% Move Speed and charge Tool and Special 100% faster while at maximum Adrenaline.

Potency and Water Damage

*SOLUTION TO POLLUTION* (Water & Ooze)

+3s Ooze duration. Enemies affected by Ooze gain 1 stack(s) of that effect every second.

After applying Ooze and Flame Damage

*SPONTANEOUS COMBUSTION* (Flame & Ooze)

Gain a 30% chance to deal 100 Flame damage when applying Ooze.

Robotics

Initial Offerings

Aggressive Savings

The more Scrap you have, the more damage you deal. Up to 100% / 150% / 200% at 2000 Scrap.

Ascendancy

Whenever you trigger a Splinter's Revive, refresh your Cooldowns and gain +25% / 50% / 80% Elemental Damage.

Blade Matrix

After reaching full charge, attack to deal 25 / 35 / 50 in an area around you.

Challenge Seeker

Get +75 / 100 / 150 Scrap when you go into a Gauntlet Challenge or Shimmering Portal.

Compound Interest

Whenever you enter a room, gain 2% / 3% / 4% more Scrap.

Laser Strike

After reaching full charge, attack to shoot a laser that deals 15 / 25 / 35 damage. Ricochets 2 time(s).

Last Stand Protocol

The lower your HP, the higher your Charge Speed (up to 50% / 80% / 120%).

Overdrive

After reaching full charge, attack to enhance your all your attacks with 15 / 20 / 30 Utrom damage for 5s seconds.

Regular Customer

Whenever you reach a Store, gain +1 Lucky Dice and 50 / 75 / 100 Scrap.

Spare Bot

Gain +1 Splinter's Revive. Splinter's Revive heals 10% / 25% / 50% more.

Survival Matrix

If you're below 50% HP, your Tool fill 100% / 125% / 150% more quickly.

Wireless Charging

Dashing through an enemy fills your Special by +15% / 25% / 35% over 2s (does not stack).

After Charge

Biomechanical Speed

Whenever your Charge Effect activates, gain 10% / 15% / 20% Special.

Charge Attacks

Whenever you Attack, gain + 10% / 12% / 15% Charge.

Empowerment

Whenever your Charge Effect activates, gain +5% / 10% / 15% elemtental damage for all attacks for that Room.

Photon Lance

After reaching full charge, attack to cause a lightning bolt to fall dealing ?? / 120 / 150 damage.

Power Surge

Whenever you use a Tool or Special, gain +50% / 75% / 100% Charge.

Synthetic Rush

Whenever your Charge Effect activates, gain 1 / 2 / 3 Adrenaline.

System Calibration

Whenever your Charge Effect activates, gain +15% / 20% / 30% Charge Speed for this room.

Thunderheart

You take no damage from Lightning Storms. Whenever you're hit by Lightning, gain 30% / 60% / 100% Charge.

Quick Study

Gain +100% / 120% / 150% Charge Speed.

After Charge and Fire Damage

*CRITICAL FLOW* (FLAME & Robotics)

Whenever your Charge Effect activates, gain 3% Critical Hit Chance for this room.

After Charge and Water Damage

*CASCADE DRIVE* (Water & Robotics)

Whenever your Charge Effect activates, gain 3% Multihit Chance for this room.

After Robotics and Utrom

*SHOCKING* (Utrom & Robotics)

After reaching full charge, attack to deal 20 Utrom damage and Stun nearby enemies for 0.8s.

Utrom

Initial Offerings

Utrom Abilities

Special and Tools deal 20 / 30 / 40 Utrom damage.

Utrom Attacks

Attacks have a 30% / 45% / 60% chance to deal 20 / 25 / 30 Utrom damage.

Utrom Battery

At the start of each Room, fill your Tool by 10% / 15% / 20% per second for 10s.

Utrom Dash

Dash deals 15 Utrom damage to 3 / 4 / 5 enemies near where you end up.

Utrom Strike

Final Strike calls lightning to hit 2 nearby enemies for 20 / 25 / 30 Utrom damage.

After Dealing Utrom Damage

Chain Lightning

Utrom damage will strike again and chain out to two nearby enemies for 10 / 15 / 20 Utrom damage.

Charged Up

Gain 1 / 2 / 3 stack(s) of Adrenaline upon using your Tool.

Electrifying

Utrom damage applies Electrifed to enemies for 3s. Electrified deals 10 / 15 / 20 Utrom damage per second. Max of 3 stacks.

Utrom Relay

Using your Special or Tool causes a Lightning Strike that deals 20 / 25 / 30 damage.

Stormy Weather

Periodically deal 15 / 20 / 25 Utrom damage to 1 nearby enemies.

Techno-Organic Interface

+10 / 20 / 30% Max Health. +15% Move Speed.

This uses your base max health without the upgraded calculated in.

After Electrifying

Alternating Current

Electrified additionally increases damage received by 30% / 50% / 70%

After Dealing Utrom Damage and Light Hammer

*LIGHT HAMMER* (Utrom & Astral Light)

Utrom damage is increased by 10% of your Max Health.

After Dealing Utrom Damage and Quick Feet

*REVOLUTION* (Utrom & Ninja)

Dash Attack's damage is increased by 1% of the enemies' Max Health.

After Dealing Utrom Damage and applying Ooze

*SECRET OF THE OOZE* (Utrom & Ooze)

Reduce damage received by 30%

After Frost and Utrom Damage

*SHATTER* (Utrom & Water)

Deal 200 Water and Utrom damage when applying a Stun effect to an enemy. Enemies are no longer Stunned.

After Robotics and Utrom

*SHOCKING* (Utrom & Robotics)

After reaching full charge, attack to deal 20 Utrom damage and Stun nearby enemies for 0.8s.

Water

Initial Offerings

Dilution

+20% / 30% / 40% Attack and Special damage area.

Still Waters

If you have not used your Attack for at least 2s gain +80% / 100% / 120% damage and your next attack is a Final Strike. Still Waters is lost upon Attack.

Torrential Strike

Final Strike grants a stack of Torrent for 4s. torrent increases Multi-Hit chance by 8% / 10% / 12%. Max 5 stacks

Water Abilities

Special and Tool has a 60% / 80% / 100% chance to deal 55 / 70 / 85 Water damage.

Water Attacks

Attacks deal 15 / 20 / 25 Water damage.

Water Dash

Deal 45 / 60 / 75 Water damage to nearby enemies at the end of a Dash.

After Dealing Water Damage

Frost

Water damage applies Frost for 5s, slowing the enemy by 50% / 60% / 70%.

Heavy Rain

Deal +40% / +60% / +80% increased Water damage. The increase is doubled during heavy rain.

Splash Damage

40% / 55% / 70% of Water damage is also dealt to nearby enemies.

Pressure Nozzle

+15% / 20% / 30% damage dealt against Bosses.

After Still Waters

High Tide

While Still Waters is active, Final Strike causes +70 / 100 / 130 Water damage and you have +15% Movement Speed.

After Torrential Strike

Torrential Rain

Whenever you use Special or Tool, gain a Torrent Stack. Your attacks deal +4 / 7 / 10 Water damage per torrent stack.

When It Rains

Mulit-Hits deal 30 / 45 / 60 Water damge.

After Frost

Flash Freeze

Frost Stuns enemies for 0.7s / 1.2s / 1.5s when first applied. Stun does not affect bosses.

Freeze

Apply Frost to nearby enemies every 5s / 4s / 3s.

After Water Damage and Light Attacks

*BRIGHT SPRING* (Astral Light & Water)

Attacks restore 2 health.

After Charge and Water Damage

*CASCADE DRIVE* (Water & Robotics)

Whenever your Charge Effect activates, gain 3% Multihit Chance for this room.

After Frost and Flame Damage

*FROSTFIRE* (Flame & Water)

Dealing Flame or Water damage with your Attack, Special, or Tool deals 30% damage of the opposite element.

After Water Damage and Potency

*SOLUTION TO POLLUTION* (Water & Ooze)

+3s Ooze duration. Enemies affected by Ooze gain 1 stack(s) of that effect every second.

After Frost and Utrom Damage.

*SHATTER* (Utrom & Water)

Deal 200 Water and Utrom damage when applying a Stun effect to an enemy. Enemies are no longer Stunned.

*This is most likely bugged and doesn't require any Utrom Power.

Legendary

I say what I believe the requirements are for each power but we can't be 100% sure until the devs confirm.

I've included screenshots where I've obtained the legendary power with a low number of other powers to help narrow down what is really necessary. If you have screenshots that can help narrow them down further please mention them in the official discord.

Many of the prerequisites mention a way to do damage. This can be from a power or a tool. I show an example of Frostfire with only Fireball and Water powers.

Some of the powers need a way to throw Shuriken. This can be from the Ninja Powers, but I've also gotten them with the Shuriken Storm tool. Leonardo's starting Shuriken doesn't seem to count though. Need more research to confirm if Ooze/Utrom Shuriken work.

The chart below shows the combinations.

DarkFlame (Astral Dark & Flame)

+40% Flame Damage against targets affected by Darkness.

Both of the starting Dark powers apply Darkness, so all this needs is any Dark power and any way to do Flame damage.

Finisher (Astral Dark & Ninja)

Attacks and Specials instantly defeat enemies that are below 15% health.

Lighthammer (Astral Light & Utrom)

Utrom damage is increased by 10% of your Max Health.

You need Light Attacks and any way to do Utrom damage.

Bright Spring (Astral Light & Water)

Attacks restore 2 health.

Light Attacks and Water damage.

This power feels more rare than the others but we don't know the percent chance of any of them showing up.

Tempered Shuriken (Flame & Ninja)

+40% Critical Hit chance with Shuriken.

Any way to throw shuriken, and Furious Attacks. Maybe it's Precision instead but I haven't been able to confirm yet.

Spontaneous Combustion (Flame & Ooze)

Gain a 30% chance to deal 100 Flame damage when applying Ooze.

A way to apply stacks of Ooze and Flame damage, maybe Inferno?

Frostfire (Flame & Water)

Dealing Flame or Water damage with your Attack, Special, or Tool deals 30% damage of the opposite element.

Fire damage and Frost

Slippery (Ninja & Ooze)

Gain 20% Move Speed and charge Tool and Special 100% faster while at maximum Adrenaline.

Need Adrenaline and any way of applying Ooze.

Revolution (Ninja & Utrom)

Dash Attack's damage is increased by 1% of the enemies' Max Health.

Need Quick Feet and Utrom damage.

Secret of the Ooze (Ooze & Utrom)

Reduce damage received by 30%

A way to apply Ooze and Utrom damage. Maybe this needs Techno-Organic Interface, need to do more testing.

Solution to Pollution (Water & Ooze)

+3s Ooze duration. Enemies affected by Ooze gain 1 stack(s) of that effect every second.

Any Water Damage and Potency

Shatter (Utrom & Water)

Deal 200 Water and Utrom damage when applying a Stun effect to an enemy. Enemies are no longer Stunned.

Obviously you need stun for this to be effective. Taunt, Turtle Line, Flash Freeze, Shocking, Core Collapse, Unfortate Odor are all the possible ways to apply stun.