Here is the full list of all 16 Shut Eye achievements.
Finish level 2
Turn on external light 10 times
Crank the music box 10 times
Finish level 1
Be scared 5 times
Chceck upper bed 10 times
Finish tutorial
Light every corner with torchlight
Finish level 3
Finish level 4
Finish level 5
Finish level 6
Finish level 7
Finish last level
Use music box in the last moment for 5 times
Listen "hero" monologue for 5 times