Flip Flappers

Cocona, a cautious middle school girl, encounters an eccentric and headstrong girl named Papika. Together, they end up traveling to strange worlds known as Pure Illusion, where they must retrieve mysterious, amorphous fragments said to grant wishes. As Cocona and Papika gather these fragments for the Flip Flap organization, they come up against Cocona's childhood friend Yayaka, who is seeking the fragments for Flip Flap's rival, Asclepius, allegedly bent on world conquest. As both organizations collide, Cocona learns more about the world than she thought possible.

(Source: Wikipedia)