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