Dotted throughout Hogwarts and the Highlands are battle arenas - the open world quest that you get in Irondale will introduce you to them, or at least one of their locations. 

On the map the icon looks like… well, depends on who you ask… it could look like a tower, it could look like someone holding their arms out with their cloak draping… you get the idea. It’s actually the latter, in case you were wondering.

There are 2 battle arenas in all (that count towards this trophy, as the Dark Arts in the Forbidden Forest does not count). One in the north and one in the south of the northern region (not including anything south of the Coastal Cavern).

The two locations are:

In order to complete the battle arena, you’ll first have to destroy all 20 vases dotted around the battle site - use Revelio if you’re struggling to see them all. Then, you have to defeat 5 waves of progressively harder enemies - for instance, the Irondale battle arena has you fighting 2 Armoured Trolls and a load of goons in the final wave, while the North Bog has you battling an Acromantula as well as a ton of other enemies.

The strategy is: go in with 25 health potions, wrack up the combos to get Ancient Power and take out the weaker ones first - so that you’re not too heavily outnumbered. Oh, and dodge… a lot!

Just be careful with the reward here, and make sure that the Acromantula isn't the last enemy you take out (unless you've already taken out his minions). I say that because when I did it the first time around, my reward (a Thief's Coat, which is needed for the Collector's Edition  trophy) bugged and didn't actually get given to me - I think because when the fight ended, the Acromantula's minions were still attacking me. I don't know the logic behind it, but I do know that the next time I did it, I killed the Acromantula first in wave 5 and I got my reward.