It says Solve 18 Melodies but you can only go to the third room, so after you finish all of those puzzles, it automatically says You completed 18 puzzles. Unfortunately, you do not receive the badge.
A lot of these daily challenges make no sense - Lead bloons and you only have a tack shooter, turret gun, buccaneer, and a monkey ace that can't put pineapples on the track to save it's life.
@ncalder97 the point of hard is that everything is more expensive, you earn less money, and more bloons come. I believe the developer wants you to buy the special building where super monkeys cost less but apprentices cost more.