I use Fang (Gaian Ring, Genji Glove, 2x Power Glove), Vanille (Gaian Ring, 2 x Weirding Glyphs, Connoisseur Catalog) and Lightning (Gaian Ring, Power Glove, Weirding Glyphs, Collector Catalog) with tier 2 weapons + Fortisol. Aegisol may help too. All weapons & accessories at star level. I manage to kill Adamantortoise in around 2 minutes.

u need to have decent setup to kill the damn toise at a decent speed. some of the things u need is :-

Fang
Must have highwind, if possible max COM role
Have Protectra,Bravera,Faithra on her SYN role
Have all the strike ability from RAV role
MUST HAVE GENJI GLOVE FOR HIGHWIND  TO BREAK THE STAGGER LEG INSTANTLY!

Sazh/Light/Snow - either 1 will do :-
Max com role or at least lvl4
Must have haste for SYN role (u can do without this but will force Fang to cast Haste on the party and slow down the kill and also your survivability)
Max Rav role
Have Imperil,deshell,deprotect on SAB role
Have CURA or CURAGA for MED role

Hope/Vanille
Have CURA or CURAGA for MED role
Have Imperil,deshell,deprotect on SAB role
Have haste for SYN role (if you have it here, then the above will be MED role)
Max COM or RAV role if possible

starts the fight with SYN/SYN/MED, having Fang cast haste+bravera on herself, then faithra+protectra on her teammate
switch to either RAV/RAV/RAV (if your party have high HP) or RAV/RAV/MED and stagger the leg
switch to COM/MED/MED and highwind the stagger leg, repeat the above and highwind the other leg
switch to SYN/SAB/SAB once the 2 legs been disable, casting bravera+faithra on everyone. wait till imperil,deprotect,deshell is stick on to toise head,
switch to RAV/RAV/RAV and get the stagger and up to 900-999%
switch to COM/COM/COM or COM/COM/RAV or COM/SAB/COM (only if you are using sazh or snow with daze, and the other COM prolly need another pair of genji glove to deal max dmg) and pummel him to death

you prolly need to have decent gears to and HP to withstand the toise stomp. get gaian ring if you are taking too much dmg or your HP is too low(you will need it later anyway to farm shalong gui anyway) and max tier2 weapon or close to max
i personally prefer fang/light/vanille cuz my light have axis blade upgraded and she has insane ATB bar recovery and Vannile has more HP than Hope. Vanille is a better choice also because all the mention role that is needed is her main role and her belonna wand makes the debuff easier to stack on the toise. but the choice is open, especially when u are near max when Hope will out damage Vanille cuz of his insanely high MAG. Snow is good too because of his high HP during your lower stat phase, but you will need to use MAG weapon for his MED role, also part of the reason I favor light.