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