I've had trouble with this, too. I recall having the same Crown setup as you. Brandt was equipped with the Red Shot and was my main attacker, Aire was the healer (obviously), and Torte was a wild card, assisting with healing when necessary, but otherwise attacking.
The Wind Cape is in that dungeon, so hopefully you use that, because Arbaroc's Aeroga seems to cause the most damage. One thing I noticed is that both the walkthrough here and the Bradygames guide suggest giving the Wind Cape to your main healer, but I disagree. The main problem I was having is that Brandt kept dying because he couldn't stand up to the magic damage. Aire and Torte had pretty high magic defense already, so they could survive Aeroga just fine without the Wind Cape. When I switched the Wind Cape over to Brandt, I had a much easier time keeping him alive, and Aire was able to use Healthgiver one turn and Cure the next, without Brandt dying in between.
So, yeah, my suggestion: give the Wind Cape to Brandt.
The first few times I tried it, I had Brandt as a Black Mage, but Fira, Water, and Aerora weren't doing much, even with Magic Mojo, and Bandit would give him more HP and Attack.
And yeah, Aire is pretty much just shrugging the spells off like nothing. It's always either Brandt or Torte that dies first, but more often than not Torte. Krinjh died pretty much right away against the Sand Devil and I just didn't bother reviving him.
So, get a Red Shot and give the Wind Cape to Brandt, and I should be pretty much good to go? No need to level up any more?
~Hurricane Legacy~ "My name is Aaron Tempest. This is my legacy."
I honestly don't remember what my levels were at that point. The walkthrough recommends levels of 17-19, though, so it might be worth your time to go kill some more stuff in the tree before taking on Arbaroc.