There's no spesific way in how to fight in the Fight Club, but since this Activity's become harder and you have to eliminate the enemies faster there's a few tips that you should know.
Try to multi kill your enemies whenever possible. This will helps you to save a lot of time than one on one attack. You can use Fire Blast on the oil drums to make an explosion.
In defend position challenge, you'll be attack by horde of enemies. I personally like to use Stomp or Fire Blast here.
In the harder level you'll be pitted against the Burning Men/ Genki's Girls. They'll keep throwing objects to you. Use Lightning Telekinesis to catch the objects/kill them.
In the final round, the main thing that you've to do is kill the Boss. Ignore the minions and keep Freeze Blast and melee the Boss, though you still have to dodge their attacks. Only attack them if they're too close or you need to regenerate health.