I'd like to suggest a mix of some of the idea listed above and my own.
I like Jotr's idea of various buildings having different types of challenges. But instead of standard pvp fights, I would like to see "game-changing" aspects introduced, each one being unique to a specific arena. After all, the Battle Frontier in the actual games introduced features which completely changed how you need to fight.
Charizard ruler suggested beacons, which plays into this idea well. One arena could have beacons as a feature. Would be interesting if they could be turned on and off to keep the battle from getting too static. Could be done on timers, on player location or action (levers and such), or whatever other ways people can think of. Ways of how to implement these beacons are just ideas I'm throwing around for people to think about/change as they see fit.
Another idea I had involves distribution of battle gear through dispensers. Each player would have a certain amount of dispensers they could activate (each one could only be activated once, of course). One each for head armor, body armor, leg armor, foot armor, and a weapon. Additionally, I think a dispenser for a random potion would be interesting.
The premise behind the dispensers is that the players will have to adapt to what they are given each round. Every battle will be different, and you can never be sure that you can rely on the same strategy twice.
Another idea to throw on top of this is having custom enchants for some items, which could potentially change how you use them. Let's say you are given a diamond chestplate which is enchanted with sharpness and fire aspect. You could either choose to wear it to soak up a lot of damage, or use it as a powerful impromtu weapon at the cost of protection. Your other equipment will also weigh in to how you choose to use it.
Those are all the ideas I have for now. If anyone else thinks it could turn out to be a good idea, feel free to improve on my ideas or add on to them. Maybe something with pigs...