In order to take off big damage in ff13 and get your 5 star ratings for the harder battles of the game, it'd be best if you could secure some 3rd tier weapons.

Every weapon in the game can be upgraded 3 times, you will have a rough idea of the final result for each weapon as you observe the grow through the first two stages. For example if you have a weapon that is growing with +7 strength and +7 magic per level up to a maximum of say 400 str and mag at the end of tier 2, then it is safe to assume that this weapon will deal massive damage as a tier 3 weapon. however if the str and mag are say 200 at the end of tier 2, then you can possibly only hope for around 500 max at the end of tier 3.

All tier 3 weapons come with an added ATB slot, giving you a total of 6. so now you can cast thundaga twice in a row! Players special abilities still take up the entire guage. Eg, Army of One will now take up 6 atb slots instead of 5.

Some of the weapons that deal extreme damage in the game have additions which are detrimental. Lightnings first tier 'organyx' turns out to be a powerful ally in harder battles, however the weapon has an addition which slows down your ATB guage. With haste on it is definately worth it, but if you ever get slow thrown on you it may be an hour before you can line up some moves (unless you paradigm shift of course)

To upgrade to a third tier weapon you again need a transforming catalyst, like Cobalite or whatever. However this is slightly more rare, it is called trapezhoereaden (didn't even try with the spelling). these can be bought from R&D Depot (which you get from completing a mission, dont remember which) for 2 Million gil. A massive ask by this games standards.

In order to acquire these 3rd tier weapons you will need a lot of cash. Because you also need money to buy components to upgrade with.

So here is what I did.

1. Farm CP to max out your players on some important roles.

My suggestion.
Lightning - Commando - Max out
Lightning - Ravager - Max out
Lightning - Sabatour - doesn't need to be max but should know- imperil, deshell, deprotect
Lightning - Synergist, would be good to know, haste, bravery, faith, protect
Lightning - Get her started on sentinel

Fang - Sabatour - Max out
Fang - Sentinel - Max out
Fang - Ravager - just get her started
Fang - Commando - Max out

Hope - Ravager - Max out
Hope - Synergist - Should know haste, protect, shell
Hope - Medic - Max out

Now you will need to take down a shit load of adamtoise and adamtortoise to earn some serious cash.. If you have completed mission 56-62 then you would have woken up the long gui and this method will be no good to you.

Now for the fights this is my paradigm set up

Lightning - Synergist
Fang - Sentinel
Hope - Synergist

Lightning - Sabatour
Fang - Sabatour
Hope - Medic

Lightning - Ravager (put lightning as your commando and fang as ravager depending on magic and attack)
Fang - Commando
Hope - Ravager

Lightning - Sentinel
Fang - Sentinel
Hope - Medic

Lightning - Commando
Fang - Commando
Hope - Ravager

Lightning - Ravager
Fang - Ravager
Hope - Ravager

Start your battle with your synergists buffing you up.

Once you have your status buffs up change to your sabatours. cast deshell, deprotect and imperil on both legs (doing leg by leg will waste time with a pointless paradigm shift) once both legs have been debuffed, hammer into one with relentless assault. Everytime the big guy decides to stomp his foot, cast quake or roar, change to your sentinels paradigm. once he has done his stomp change straight back to relentless assault, do not get stuck healing to much. just make sure to be quick at changing paradigms jus before he executes a move.

if you have fang as your leader (and a genjo glove equiped) once you have staggered a leg her highwnd move will take it out. If you have lightning as your leader then just stick with relentless assault until both legs go down..

Once they are down quickly change back to ur sabatours now cast, slow, imperil, deshell and deprotect on his head. once this is done change to your three ravagers to stagger. Once it is staggered hit it with Army of One, if you are using lightning as your leader, you may have to use army of one twice to bring the chain gauge up to 999, but once it is change to aggression (2 commandos, ravager) for the kill.. if you do not kill it then simply repeat the steps.

Each battle should take around 2.5-3.5 minutes if you kill him on the first fall and around 6-7 if you dont take him down till the second fall.

nevertheless you will gain a lot of gil and some traps for upgrading to your third tier weapons.

Good luck