Here is the full list of all 12 Home Improvisation achievements.
Shatter the vase.
Turn the lights all the way down.
Build all furniture pieces.
Unlock all rooms in the house.
Unlock all tools.
Complete all challenge levels.
Build all furniture in a room.
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.