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