Here is the full list of all 19 Darksy's Adventure achievements.
Buy the Speed Boost ability
Defeat General Foxin
Beat the first level
Defeat the Caracal Pirate
Defeat the Wild Furry West Police
Defeat the Dog Police Commander
Defeat the Bobcat Robot
Defeat the TV Tron
Reach a completion score of 100%
Buy the Magnet Ability
Buy the Super Darksy ability
Buy the Invisibility ability
Find all retro cartridges
Beat all retro minigames
Beat all of the levels without grabbing any checkpoints
Beat every level while collecting all atoms
Beat every level without dying
Buy all of the accessories in the shop
You beat all of the levels. Sit back and relax!