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