Legends of the Flaming Falcons

[Pherione]

@MetalRenard: It's not a bestiary, the bestiary is another part of the extras menu and is where the normal monsters are shown.
The cards are for one of the minigames: Radia Battles, you can collect them and use them to power up your Radia Battles monster which you pick when you first start playing the minigame. There aren't only monster cards, but also equipment, character, area and skill cards. They all have their own unique effects when you apply them to your monster and certain card combinations work better than others.
So your first idea was right, they have to do with the minigame battle system.