You don't need 'white mage stuff' on the Champ per se, but you absolutely should have a healer in the party for any dungeoneering and bringing a source of Holy damage to the dungeon filled with demons that are massively weak to it is kind of a no-brainer. One the game even reminds you of before you set out.
That said, if you're stuck in the dungeon with a bad setup and you can't conveniently reload a pre-dungeon save, your best option is to turn the difficulty down to Story, at which point you should be able to sleepwalk through the fight with Alissa.