Recently I had a lot of trouble find a good party and paradigm combination to kill adamantortoise, but with this method he can be fallen anywhere between 4-10 mins. I was mastered in all three main roles, and almost mastered in a 4th role for everyone.

Your party should consist of Fang/Hope/Lightning, with Fang being your party leader.  Equip Fang with a one or two clay rings, or its upgraded form, and do the same for Hope, since he has the least health, and equip Lightning with accessories that reduce damage. Also, have the "Random Instant Chain" ability for both Lightning and Fang. Hope will act mainly as a medic for most of the battle until the legs are disabled. 

Recommended Paradigms:Fang/Hope/Ligntning







Start the battle in Evened Odds and have hop cast Protectra and Haste on the party, then Bravera herself.  Make sure that Imperil and Deprotect has been casted on the leg, if so switch to Diversity, and when you Stagger it, and get it to about 30% health, use Highwind and will finish it off.  Then switch back to evened odds, and rebuff since the buffs will wear off shortly after the first leg is disabled.  Then do the same to the right leg, making sure Deprotect and Imperil are inflicted.  Once the legs are disabled switch to Sab/Med/Med and cast all status ailments with Fang (Slow,Deprotect, Deshell,Imperil), and then switch to Relentless Assault then once it Staggers wait to about 800-850% and switch to Aggression.  If the Genji Glove is equipped he is easier to take down in one Stagger, but when hes standing up, use Highwind, and if he lives just repeat the process. 

The battle will take 3 mins if you get the random instant chain quickly after he falls, and if he needs to be staggered a second time it will take you on average 10 mins.