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