The most important thing to doing this fast is probably having a Genji Glove. This goes to Fang. Also put on her whatever collector's item you want (whether going for money or catalyst). For the other two slots, I'd suggest the best phys resist item you have, though I'm going to experiment and see if this is really necessary. My Fang had 44% physical resist.The other two people in your party just need to be decent Ravagers. The only thing they really need is phys resist gear, and the more of it the better. Growth egg if you need CP.You only really need 3, maybe 4 Paradigms (which you can mirror and paradigm change for instant filling of ATB gauge).1) Combat Clinic: Sentinel/Medic/Medic. 2) Relentless Assault: Commando/Ravager/Ravager3) Aggression: COM/COM/RAV4) Something that makes Fang a synergist (and you have at least Bravera, if not also Haste) I use a party of Fang, Lightning, and Vanille.Start off the battle with 1) and wait for him to stomp. With phys resist, and Fang as sentinel (she has fringeward, which reduces group damage from area attacks). It might do 3-4k, which will be quickly healed back.Once healed, switch to 2). Let fang hit the leg once or twice while the other two cast magic. Switch back to 1) and wait for the stomp. Heal and go back to 2). At this point, the leg should stagger. Immediately use Highwind. If you have genji glove and high enough STR, you will instantly destroy it. Just repeat the cycle for the other leg.
Once he's down, debuff him with Fang and Vanille (imperil, deshell, deprotect, slow), and buff up Fang and Lightning with Fang's uber buffs (VAnille has them too, but you'll want to control this part). Haste and Bravera. With him debuffed, and you ultrabuffed, you should be able to kill him with Com/Com/Ravager [though you may want to go back to Relentless Assault briefly to get the stagger gauge up higher). Now, he won't stay down so long as with a summon, but another highwind at the least should finish him if he gets up before stagger ends. If he does, no big deal, just restart the cycle from the beginning. I've just starting doing this and I'm killing him in less than 3 minutes. This method should work even better for Adamantortoise, who has less hp, but more imporantly, whose legs have 100k less hp and way easier to stagger.