He's very tough, I would beat the game before taking this guy on.  You should probably also be at the maximum role levels for your characters.  Wear items that protect against earth, and kill its legs first.  I haven't tried these, but RAV/RAV/RAV is a great way to get it to to Stagger after you hurt its legs.  I've also read that you can exploit him by casting "death" over and over with Vanille, but I haven't tried that either.

Play as Vanille, and get your summon out right away. This will topple him to his knees. Now get him deprotected, deshelled and imperiled. Spam death. If he gets up, restart and retry until he dies :P

Yes the cheap way to kill him is to let Vanille learn Death.  
 
Have your team as SAB/SAB/SYN.
 
At the start of battle, use Vanille's summon.  Adamantoise will then fall to the ground.  Use this time to cast Death over and over again hoping that it will 1-hit kill him.  When the Summon is over, your SAB and SYN will pop back in with full health.  SAB will de-buff and SYN will buff up the team.   Keep Vanille casting Death.  
 
If Adamantoise gets back up and you still haven't killed him, you will have time/health enough to withstand 1 stomp hopefully.  After that stomp if he's still alive, then press Start and Back/Select to retry the battle.

I used Fang/Hope/Lightning, stacked +STR items on Fang and Lightning, started the battle with Haste on Fang and called Bahamut.  Have Fang go SAB and debuff the hell out of the turtle, then when the summon's meter is almost empty go into Gestalt mode.  You should end up taking about 1mil from the turtle from the summon.  
 
Then return to battle in SAB/SYN/RAV and buff up everybody and debuff the turtle some more.  Switch to COM/RAV/RAV (or RAV/RAV/RAV if your Fang has rav skills) and stagger him, then switch to Com/Rav/Rav to hopefully finish him off before he gets back up and destroys you.  This sometimes works, and sometimes he gets back up and kills you.  Still, this is a little less cheap than the Death method.

Does imperil, deprotect or deshell affect how often Death will work?

" Does imperil, deprotect or deshell affect how often Death will work? "

I always use Lightning, Fang, and Hope. Lightnings good at both Strength and Magic, Fang is good at Strength, and Hope with Magic. I haven't fought this beat yet but your best bet is use Evened odds to cast debuffs and buffs. Then go with (don't remember the Paradigm) COM/SEN/RAV till he's about 50% through his Stagger gauge. Switch to Mystic Tower to bring up to full faster. After he's full then switch to Relentless Assualt and go all out. If you get hurt too much then go with a Combat Clinic. Just have patience and it should fall.