well i watched the battle system movie again and i think i sort of can explain how the system itself works
it's a turnbased system so you get your turn, then the enemies get to attack and so on...
basically battles seem to start with your turn first, and you have a limited amount of time to select your attacks (based on the cards delt to you)- i would say you get to order your cards, but it seems like they are reshuffled every turn so you must make use of what you have- you try to string cards together in your time frame to form combo attacks and do more damage, but after attacking, it seems like they try to keep you on your toes, so you have to choose cards for defense as well- basically you must choose the cards before the enemy's attack takes place- then the enemy attacks you- based on the defense you choose, you could limit the damage you take- this is all shown on the screen after every attack- it shows how much damage the enemy inflicted on you, then it shows next to it the damage taken away based on your card choice- it seems like a very interesting system indeed and i hope this game comes out in america- i really want to play it