Here is the full list of all 21 The Many Pieces of Mr. Coo achievements.
Beat the game without hints
Beat the game
Everyone plays the piano
Escape from lava
Many dead pieces
Get it
A circus trick with a seesaw
Free the lady
Free the faun
Free the legs
Take the legs upstairs
Find the torso
Eat the apple
Get cut in 3
Exit the egg
Many attacks from the little chick
Open the present
Solve the arcade puzzle
Legs prank head
Get the first paper
Get 100 papers