One you've made some progress in Cauldron, you'll come across the minecart minigame which takes the form of a 'Survivors-like'. Unlike others of the genre, you get to freely pick and choose which attacks and abilities you acquire. All attacks and abilities come from the characters you've collected so far in your adventure, during the minigame each of these characters are placed randomly around the level for you to find.
Although, right now there's no in-game description of what each of them do, you can make a guess based on their normal combat abilities but sometimes it can be hard to tell what effect they're having. So I've made a list of what I think each character does, hope it helps!

You always start out with Nyx in the cart. If you want you can eject her by using the menu option.
Shoots a basic projectile towards the nearest enemy. As you level up Nyx, she will shoot additional projectiles.
Shoots elemental projectiles in every direction causing burn, freeze, spark and poison.

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Attack all enemies near the cart, the size of this attack increases as Froggy levels up.
Attack all enemies on the screen.

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Shoot arrows in all directions around the cart. Shoots more arrows and arrows gain piercing as she levels up.
Shoot lots of arrows in all directions.

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Attack all enemies near the cart. Does low damage but high knockback.
Attacks all enemies in a much larger radius around the cart.

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Restores health.
If the cart's health reaches 0 while this special is fully charged, the cart will be revived.

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Creates shields which orbit around the cart, damaging and knocking back anything they touch, but will break after a few hits.
Will add and slowly restore, essentially, a second health bar.

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When this triggers, one member of the cart will have their skill recharge speed up for one second.
All members of the cart will have their skill recharge speed up.

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Places a torch down nearby the cart, when an enemy touches the torch it will receive burn damage.
Shoots out flames in four directions, doing burn damage.

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Attacks a random enemy with spark damage, causing the damage to spread out and attack other nearby enemies.
Shoots out projectiles that will pass through enemies and bounce off the corners of the screen, doing spark damage.

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Places a toxic puddle at the nearest enemies, doing poison damage to all that pass through it.
Places a giant toxic puddle centred on the cart, doing poison damage to all that pass through it.

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Shoots a projectile towards the nearest enemy, doing cold damage, freezing the enemy in place briefly. The projectile passes through enemies.
Shoots cold projectiles in all directions.

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Shoots an axe projectile that will pass through enemies and bounce off the corners of the screen.
Spinning blades surround the cart damaging anything they touch.

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Does high damage to a random enemy on the screen.
Does high damage to a handful of random enemies on the screen.

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Restores a small amount of dash.
Each time this triggers, a permenant (for the round) +5% bonus is added to each crystal picked up.

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Copies and uses a skill picked randomly from the other characters in the cart.
Will copy and use the next special skill performed by a character in the cart.

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Shoots projectiles in a circle all around the cart, doing low damage but high knockback.
Collects all crystals in the level.

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For a short time all damage done by other characters is buffed (~+20% damage at base, ~+50% damage after 5 upgrades)
Each time this triggers, a permenant (for the round) +5% bonus is added to all damage.

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Enemies will be slowed in a small radius around the cart.
Each time this triggers, a permenant (for the round) +5% bonus is added to defense.