To gain different ranks, you will need to level up a certain amount of times. Each rank up allows you to choose one-time special bonuses to apply to that brother.

Rank	How to unlock
Boomerang Rank	Reach Level 12.
Flower Rank	Reach Level 19.
Leaf Rank	Reach Level 27.
Rainbow Rank	Reach Level 46.
Shell Rank	Reach Level 6.
Star Rank	Reach Level 36.