Here is the full list of all 14 BiT Evolution achievements.
Complete 20 levels in the game's challenge mode
Defeat the game's final boss
Defeat the boss of World 4
Collect all of the pixels in the game
Defeat the boss of World 3
Carry the first Spider Clam to the goal tape on level 3-11
Defeat the boss of World 2
Complete a level without ever entering the Realm of Code
Defeat the boss of World 1
Find any hidden area within the game
Survive 30 seconds with the "death wall" in level 1-11
Obtain a gold star on any 10 levels
Complete a level without killing any enemies (not even bats!)
Obtain a gold star on any level