There are three arenas that you'll unlock while playing through the game. Two of them are mementos that you'll have to find or buy from the Lost & Found, if you didn't get them in the area. The last one will be unlocked as part of the story. They are all on the south side of the bastion. Just press when next to them and fight you're way through the 20 waves.
It's best to wait until the end. I like to use the upgraded shotgun, because it is quick, does a huge amount of damage and can kill a whole bunch of enemies at once. You should also equip a few good potions. Get one extra try and 2+ water bottles. this will make the arenas much easier.
Utilise the roll and counter attack (blocking with when the enemy attacks you). This will instantly kill the towers and some weaker enemies.