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