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