There are a number of strategies to use for them. I recommend maxing out all of your jobs and your three monsters having more then 2000 HP.
Monsters
- Vodianoi level 17
COM
- Gremlin level 40
RAV
- Green Chocobo level 27
MED
Accessories
Noel was 3 Power Wristbands and for Serah I used Hypnocrown, Durable and Delicate Magician's Mark.
Paradigms
COM COM COM Cerberus
RAV COM RAV* Relentless Assault
RAV SAB RAV* Smart Bomb
RAV COM MED* Diversity
SAB SAB MED* Safe Subversion
MED MED MED Salvation
The ones I've starred are the more critical ones I used. The all COM paradigm is nice to have if you cannot finish them before the stagger bar empties.
The fight can be broken up into three parts one is when, Lightning is alone and you just need to get her hp down to about 3/4 which isnt very hard, and the second phase is when Amodar joins the battle (COM COM) the two of them work more on party damage with Amodars grenade or him simply attacking all party members if close enough. Lighting dealing party damage with Ruinga. After about 2 mins in they change to either SAB SYN, SAB MED or COM RAV. When Amodar is a SAB he inflicts just about anything on the party member he attacks so I recommend going after him first, plus Lightning is easier to take out alone without his debuffs.
At the start of phase two I recommend either RAV SAB RAV if you think you're good enough, or SAB SAB MED to keep more HP. (Note my chocobo did die often so have many phoenix downs and potions, possibly if you desire remedys) you can only inflict Deprotect and Deshell on Lightning and Imperil and Poison on Amodar however you really only need Imperil. Once you have that on Amodar, switch to either RAV COM RAV or RAV COM MED and stagger him. He does have a lot of HP but if you either get his HP to 999.99 or about 1/3 of the way empty change to COM COM COM and you should be okay. This also works on Lightning, however Amodar like to switch to SAB and cast a lot of debuffs on your party.
Now comes the third phase, either Lightning or Amodar are alone and they cast a few buffs on themselves which cannot be dispelled. I recommend switching to RAV SAB RAV and repeating the above on them, and then switch to RAV COM RAV and try to stagger them. Before you can, they usually get off about 2 Feral Links but Lightnings is weaker and wont instantly kill your party members (except Noel). With this party I recommend having atleast 20 Phoenix Downs to revive your monster and Sarah or Noel if they die.
Yes, it does affect a few things.
First, if you make a clearly goofy selection you'll get a Live Trigger Reward other than a potion. Why this is doesn't make any sense to me, but picking the right or logical answer won't net you anything. The rewards here are almost always cosmetic so you're not missing much of anything.
Second, some of the live triggers will result in a Paradox Ending. These are, simply put, bad endings to the game. When you come into a Paradox Ending there will be a short scene and you'll be dumped back to the Historia Crux.
The unique thing about FF 13-2 is that all of these choices can be replayed by closing and opening gates again. Everything in the zone gets reset other than key items and fragments. So if you're not satisfied with how your first choices turn out you can simply go through it again.
Best Answer
I killed Lightning first both times just because that guy is an absolute tank and got both of them. Helps if you have that mog extra to make turning enemies to crystal easier.