I'm having a serious field day on Final Fantasy 13 right now. w00t
For those of you in the know, when roaming around Pulse on chapter 11, you eventually encounter the huge Adamantoise species. There's no use fighting them unless you've got very strong equipment and have filled up a lot of your Crystarium; they're just way too powerful and can kill your party in one or two area of effect attacks. Anywho, they ARE defeatable.
You'll want to challenge them after completing Stage 9 of the Crystarium and acquiring each character's ultimate skill.
Lightning: Army of One [Ravager]
Hope: Last Resort [Ravager]
Sazh: Cold Blood [Ravager]
Fang: Highwind [Commando]
Snow: Sovereign Fist [Commando]
Vanille: Death [Saboteur]
You can take them out in one of two ways. You should enter the battle with 3 TP. You could also activate the Fortisol shroud to start the battle with Bravery, Faith, and Haste. You'll also need to start in a paradigm that has Fang as a Saboteur.
One is a pummel without abandon approach; the other is Death. Here's how.
For the first, get Lightning, Snow, and Fang in a party; Sazh is a good substitute as his Blitz [Commando] move can hit huge enemies many, many times. Immediately start the battle by summoning an Eidolon. The Adamantoise creatures will collapse before them. Fang should spend the time piling on as many debuffs as she can. This will raise Bahamut's gauge to full. When shifting into Gestalt Mode, immediately perform his final move which will hit for at least 200,000 HP damage. (No worries; very small potatoes as Adamantoise creatures have at least 3.6 million HP.)
While it's down, shift into Relentless Assault [one Commando, two Ravagers] or Tri-Disaster [three Ravagers] to max out the gauge. If you've got the passive skill Random Instant Chain, it makes it even easier to stagger quickly. Build as fast as you can, then shift to Cerberus [three Commandos] and just pile it on! It'll fall.
The other approach is to put Vanille in the lead. You'll probably want a paradigm setup like Espionage [two Saboteurs, one Synergist]. Again, summon your Eidolon immediately to get it to collapse. Personally, I like trying to off it before my team shows up. To do this, Vanille inflicts Imperil and then repeatedly casts Death; if under Haste status, you can try between 5 and 7 times.
When the party returns, the other Saboteur, probably Fang, will work on casting other debuffs and your Synergist can enhance the chances of a successful Death cast by casting Vigilance and Faith.
While this method is based on luck, the upshot is that you don't have to waste a shroud before battle begins. That, and the toughest Adamantoise has too much health. It's hard to beat into submission.
The downside to either of these approaches is that should the Adamantoise get back up, it's coitans. Just pause, press Select, and retry the battle; spare yourself a Game Over screen. On the plus side, the wins are worth it. Both of the larger Adamantoise creatures grant the same rewards -- 40,000 CP and a chance to drop a Platinum Ingot [which sells for 150,000 Gil] or a Trapezohedron [which is the rarest, most expensive catalyst mineral used to transform your level 2 weapons into their ultimate forms].
Finally, some additional information about how I set up and equip my teams:
Pummel Approach:
All members carry Sprint Shoes -- this gives your team auto-Haste at the start of battle. Two members will also wear Speed Sash and Energy Sash. These accessories give extra ATB and TP for successful kills; combined, they also allow random instant Stagger. One person on the term should wear the Collector's Catalog and the Connosieur's Catalog, which ups the chances to getting the Adamantoise to drop a spoil (the Ingot is common; the Trap is rare, respectively).
Death Approach:
Same accessory setup as before. Vanille should wear the Belladonna Wand-line of staves as this improves her debuffing abilities. (Strange that Death is a Saboteur spell; it counts as a debuff... that can kill *dun dun dun*.)
Okay, dorkiness complete.