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