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