After you've unlocked a Rider then find the Rider with the card in the their deck in Mirror World and defeat him or her for the card (e.g. for Wing Knight's Nasty Vent, you must fight him when he has the card in the Mirror World).

Complete Arcade Mode with the 6 Riders to unlock additional Riders. Play through Mirror World as Dragon Knight and Wing Knight to unlock their Survive Modes. Play Arcade without losing to unlock Wrath. Play through Arcade as Wrath and don't lose a single match to unlock Onyx.