In the final part of the Luxord fight when he hides in the cards, the aim of the game is to constantly eliminate the potential cards he hides in using Triangle and avoiding damage.
However, you are on a time limit. The circle of cards that surround you, which Luxord hides in, gets smaller and smaller, both from you eliminating cards he's hiding in, and him eliminating cards to surround you.
Your goal is to consecutively find Luxord in cards with Triangle at least 5 times in a row while not dying, losing all time, or letting the circle get so small, Luxord declares victory.
The best way to do this is to use the time-slowdown that happens when you shotlock. This allows you to circle the camera in slow-motion and see where he's hiding.
In the final part when he actively begins to attack you from cards, keep moving and be precise where you hit triangle to eliminate him before you take damage, and prevent you from hitting triangle on the wrong card. If you do it right enough times, he'll concede, be open to a combo, and usually you'll finish the match from there. If you don't, then basically ALL his games become harder. The magic game that usually required you to use Thunder to eliminate his cards, will require fire. The circle of cards that surround Luxord, which require you to hit the card with O behind it, will be far wider.
So yeah. Try to eliminate him during his Limit Break move or shortly thereafter. This fight took me the most time to beat too. I don't know why but it fucked me up.