Hm, when I did it I was just fine with one Dargoon. Garuda absolutely destroyed the rest of the party but my Dragoon took him out almost single handedly.

In all honesty, healing in that fight is just about a complete waste of time. Just race to land as much damage as you can as quickly as you can. You can also move the dragoons to the back row, as they will deal just as much damage using Jump from the front or back.