In the end, we won by the skin of our teeth, by abusing Mage's Ballad, a Dragoon's Level 2 Limit Break, and one of the best healers I've seen in the game. While difficult, the boss is very satisfying upon completion, and makes you value your job classes that much more. I can only look forward to future dungeons and what kind of strategies I will have to develop in order to solve them.