In my view, there are three tiers of Adamantoise strategy. If you're maxed out on the Crystarium for your three main roles, you're ready to graduate from Tier One (SpamDeath) to Tier Two (SpamBlitz).
In order to SpamBlitz you need a couple of things. Make a part with Sazh/Lightning/Fang, with Sazh as leader. If Sazh's STR is not at least 1200, you have more leveling to do. I got his strength high by fully upgrading the Hyades Magnums (I think, whichever weapons provide the greatest boost to STR). You'll want the following Paradigms:
SYN/SAB/RAV [Guerilla]
RAV/RAV/RAV [Tri-disaster]
COM/COM/COM [Cerberus]
Start with Guerilla. As soon as you enter the battle, summon Brynhildr. While your summon is out, hit it with Deprotect/Deshell. The key here is to NOT Stagger the Adamantoise while your summon is still out, otherwise he will just stand up. Dismiss Brynhildr when you are close to Staggering, then Stagger is once your party comes back.
Once you Stagger it, switch to Tri-disaster and use Sazh's Cold Blood ability once to drive the turtle's Chain up, then switch to Cerberus and spam Blitz until the turtle dies. It should only take one Stagger to accomplish this. If you can't do it in one Stagger, keep practicing...you'll get the timing down pretty quickly.
Good luck.