Here is the full list of all 27 The Little Ball That Could achievements.
You've completed all tasks in Purple World.
You've gone through Purple World.
Collect all items in the level and die before reaching the end.
Complete a level without activating any checkpoints.
You've gone through Blue World.
You've gone through Green World.
You've gone through Yellow World.
You've gone through Orange World.
You've completed all tasks in Blue World.
You've completed all tasks in Green World.
You've completed all tasks in Yellow World.
You've completed all tasks in Orange World.
You chose to wander the world with your friends.
You chose to rule your kind.
Break on fall or impact 100 times.
Drown 100 times.
Get killed by mechanisms 100 times.
Complete a level using the Speedy power.
Complete a level using the Armored power.
Complete a level using the Jumpy power.
Unlock all skins in the game.
Complete a level in under 10 seconds.
Start the Game+ Mode.
Restart from a checkpoint 10 times in a single game.
You've completed all Time tasks.
You've found all Puzzle Pieces.
You've collected all Gems.