Here's a guide for killing an adamantoise if you guys need help. This is WITHOUT using a summon.
Characters:
Fang(You)/Light/Hope or Vanille
Paradigms:
RAV/RAV/RAV - Default
SEN/SEN/MED
SAB/SAB/SAB
COM/COM/RAV
SYN/SYN/SYN
SEN/SEN/SEN
Weapon for Fang:
Kains Lance - Upgrade Dragoon's Lance or Taming Pole to get this, and then max it out. You want Fang to have 2700+ Attack.
Equip these accessories on all your characters:
Tetradic-Tiara
Speed Shoes (What-ever one gives auto-haste)
Att + Mag up for the specific characters. Attack accessories ONLY on Fang.
The item drop rate items. Only 1 of each can be put on your entire party, they will NOT stack.
Process:
Start off by damaging the right leg with RAV/RAV/RAV. Stagger it to about 600% and then Highwind it for an instant kill. Switch to SEN/SEN/MED because you need to heal that first stomp.
Switch back to RAV/RAV/RAV and go for the left leg, but watch as the Addy is going to try to stomp you and you NEEED to switch back to SEN/SEN/MED as soon as he does. Repeat 600% process on left leg.
Now he is going to fall, immediately switch to SYN/SYN/SYN no matter what your health is unless you have like 1k left. and put Bravery/Haste on Fang, and just Bravery on Light. Hope should have all the Haste for the party taking care of.
Switch to SAB/SAB/SAB. You need to put these 3 and ONLY these 3 effects on him. Imperil (Which you should cast), De-Protect, and De-Shell.
Switch to RAV/RAV/RAV and stagger his ass to 900%. Switch to COM/COM/RAV. and WAIL on him. If you do this process fast enough you can kill him before he gets up. But if you see him get up, HIGHWIND him.
You may lose once and awhile because your not used to process, but once you fine-tune it. You are unstoppable.