**WARNING: SPOILER MATERIAL AHEAD FOR FINAL FANTASY XIII**
Okay. This guy was the first boss I hit that was a real bitch to take down, that I had no idea of how to beat, until I learned a simple little trick. But I’ll give you the whole strategy first, and I’ll highlight the trick for you when it comes along.
My battle team was Lightning, Snow, and Vanille.
First, attack his appendages. You can’t hurt the main boss until you’ve beaten the appendages. So, go ahead and beat those. Whale on them. Stick to Relentless Assault as your paradigm, switching into a healing paradigm whenever you need to.
Once the appendages are done, you’re going to want to try to take this guy down as quickly as possible, as he can randomly cast Doom on you. If he randomly casts Doom on you and he’s at like 50% health, forget it, just die and try again.
Stay in an offensive paradigm as much as you can and deal as much damage as you can to this boss. Switch to a healing paradigm whenever you get a little low on HP.
Now, here’s the trick to getting past that goddamned “Destrudo” attack that takes all your characters’ health down to zero and makes it game-over time: While he’s charging Destrudo, do not, I repeat, do NOT go into a defensive paradigm of any sort. Go with Relentless Assault, or even Tri-Disaster if you so choose, and whale on the guy while he’s charging the Destrudo attack. Once you deal enough damage, you’ll hear him scream, “Aaaahhh!” briefly, and you have then weakened his Destrudo attack sufficiently so it will not kill your entire party. Then I suggest going into a healing paradigm, perhaps even Combat Clinic (two medics), and heal yourself while and after Destrudo is unleashed.
Without knowing how to weaken the Destrudo attack, this guy is impossible. Not very fair, Square-Enix, not very fair. 
Good hunting.
Use,
Lighting/Sazh/Hope
Relentless assualt/diversity
get rid of the face things then get him into stagger. Once in stagger use Odin then go into diversity. Just before he realises doom use ur potions and do that as often as you can if you cant continue attacking because it seems to miss you when you are attacking.
Yeah, but if you can do enough damage while he’s charging his overdrive attack, you can make the attack weak as all heck (following the directions I put in the post). But your scenario is also workable — it’s just that getting rid of the Overdrive attack (well, making it basically very small in terms of damage) works faster. Game on, bro!