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