Here is the full list of all 21 The Many Pieces of Mr. Coo achievements worth 1,000 gamerscore.
Solve the arcade puzzle
Open the present
Many attacks from the little chick
Exit the egg
Eat the apple
Get cut in 3
Everyone plays the piano
Legs prank head
Escape from lava
Find the torso
Free the faun
Free the lady
A circus trick with a seesaw
Get it
Take the legs upstairs
Free the legs
Many dead pieces
Beat the game
Get the first paper
Get 100 papers
Beat the game without hints