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