Setup:
Xon : Lakshmi + Cradle of Horns + Enhanced Twist of Fate
iNichol : as much SPR as possible, as much LS/turn as possible, as high LB level as possible
LMS: Rikku's pouch
These 3 characters will control all the damage for you except the "Black Flames" later in the fight. I'd say you need at least 6k hp on your characters to withstand that attack, or you need to bring a stronger MAG breaker than 45%.
First 4 turns:
iNichol = Cover + break, Cover + break, LB, Cover + break
Xon = Cradle of Horns, Assuring Protection, Cradle of Horns, Twist of Fate
LMS = Guard, LB, Panacea, Guard
Every 4 turns after that:
iNichol = LB, Cover + Break, LB, Cover + Break
Xon = Free Turn, Assuring Protection, Cradle of Horns, Twist of Fate
LMS = Eccentrick, LB, Panacea, Guard
Substitutions:
Ditch Lakshmi if all characters are confuse immune.
If you bring a magic user, make sure you can get very high fire resist (100% ideally).
You can leave Rikku's pouch off LMS if your characters are status immune and you're not worried about LB fill rate.