The arena fight is forced at midnight on Day 2/3/4, where you are teleported to an arena to fight 2 mini-bosses - the Black Reaper, the White Reaper, a bull-like creature, and a bird-like creature.
Before being transported to the arena, go into the starting area casino, left of the stone stairs, and use the ATMs and vending machine to get chips. There are also 2 ATMs and a vending machine near the fountain in the starting zone. It's best to get 2 green chips and a red chip as a backup, but if you need more chips (preferably green chips) you can revisit the ATMs and vending machines every hour for more chips.
Once force teleported at midnight, line up next to the enemy on the left side and use a green chip once it spawns. Lock on to the enemy using
and swing away with the temporary infinite stamina. It should go down around the end of it running out. If the enemy isn't pushed towards the 2nd enemy, the 2nd enemy will run away or stay put and not engage you. Switch out to the 2nd enemy and repeat, and the win should be earned.