Battles are 1v1 so that portion plays like a card game/ turn base battle. These fights can be pretty quick unless you are running a tournament. The Story Arc portion is more of a collaborative RPG. You could treat it as a solo RPG but I think it's better when you include another player in it.
Combat breaks down to one fighter choosing a move from their list to attack with, rolling to see if they hit, then their opponent choosing a move to defend with, rolling to see if they block/soak or deflect and counterattack. Roles are reversed and you go back and forth until one of the fighters' Power Level hits 0.