The arena DLC is actually not bad. Depends how much you enjoyed the combat in the game I suppose.|
I personally thought it was great, and this is just more of it. If you die in the arena you can choose to continue but forfeit your score, which is fine by me since I don't much care for leaderboards. You earn money for combat, which includes kills, looting, environment kills, chaining vigors, that sort of thing. Everything you earn and the upgrades you unlock are done as an overall progress and not per arena, so there's a gradual sense of progression even if you're stumbling through it. Once you clear the first arena you get access to the museum area where you can purchase artwork and music.
The arenas involve 15 waves of enemies. If you really don't like combat you won't enjoy it, it took me about an hour to clear all 15 stages. It's quite hard too, especially the final stage which throws two handymen + a patriot at you. In between rounds it alternates between giving you an upgrade potion (health/shield/salts) and a piece of equipment. I only had time to do the first arena but I assume by the time you've beaten every wave in every arena you'll have obtained all the items and will be fully upgraded.
All in all, it's pretty nicely put together. It was quite a good idea to keep this secret and release it on the same day as they announced two story DLC's. I don't think many people care for arena DLC's, but it's easy to see why they exist. This'll do for now.