@jaclcsparrow: I just got the medium badge. There's only three rooms and 18 melodies. You may have missed a few pieces. If you wait, you will see some places that shine: it indicates you pieces you've missed. Good luck.
I don't get the logic behind the pets order. The first one is better than the second and the third, so you have to buy to useless pets to be able to buy the forth... And you repeat the cycle.
Two solutions : you give better stats to the second and third one, or you put the first one on the third position.