Instructions
Win at least five battles in the game's "Story" mode.
Press the "Start" button to open up the game's menu.
Select the "Build Deck/Chest" option, and press the "X" button.
Find a card you would like to reincarnate. Only cards that have a flashing white message under them saying 'REINCARNATION" are eligible to be reincarnated.
Highlight the card and press the "L3" button. This button is not on the controller; press it by pushing the left analog stick inwards. Doing this sends your card over to the chest where it will be reincarnated into three cards of varying value.