Remember that after you've staggered it, build up some nasty high percentage with Sazh's or Lightning's signature moves. Then go all nuts with the strongest possible combinations (lots of commando's). If your having Fang as your lead, do Highwind when the stagger bar is about to disappear but make sure she does it while the enemy is still staggered.
To quickly buff up, use two synergists and a saboteur. Saboteur's build up and maintain stagger pretty good. Or if you only have 1 synergist, then use one synergist, one saboteur and one ravager for excellent build stagger build up while your buffing.
You should only buff up with Haste, Bravery, and Faith. That should do the work for your damaging business.