Here is the full list of all 12 Home Improvisation achievements.
Use the mallet to break something.
Build all furniture in a room.
Shatter the vase.
Turn the lights all the way down.
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.