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