Here is the full list of all 12 Home Improvisation achievements.
Build all furniture in a room.
Use the mallet to break something.
Turn the lights all the way down.
Shatter the vase.
Build all furniture pieces.
Unlock all rooms in the house.
Unlock all tools.
Complete all challenge levels.
Play every note on the piano.
Complete the Speed challenge level.
Complete the Height challenge level.
Complete the Shatter challenge level.