I had trouble the first time I faced the last boss. I was slightly underleveled and didn't have anything close to a dream team of pets. Other hassle I ran into was that I played 99% of the game with my pet being a SEN. Which of course the last boss has almost no use for SEN except for reducing damage taken during big attacks.
My first tip would be to examine your characters and pets. In classes, I made sure I had at least Serah complete in Ravager and that I decked her out in the best +Magic I had. For Noel I made sure his Commando was complete and decked out in +Attack.
For Pets I had Gold Chocobo (COM), Cloudburst (RAV), and Pulsework Gladiator (SEN). Of course, deck them up in best stats; +Attack for Chocobo, +Magic for Cloudburst, and +HP for Pulsework. Pulsework's special is pretty useless, but utilize Cloudbursts and Gold Chocobo's every chance you get. FYI, Cloudburst and Pulsework are in Archylte Steppe ???AF, Golden Chocobo is in Dying World 700AF.
Some good tips during fighting the last boss:
-Keep in mind that Potions in this game are extremely useful. Fill your inventory with as much potions and wound potions as you can carry. Use them to keep yourself healed without having to resort to switching to MED. If you're confortable with using potions, you can even experiment with getting Serah a grimoire hat and use her in battle to get the most out of your potions. I used this method to beat the tougher bosses in the game (there are some!).
-If you see the boss building up for his big attacks, switch to SEN/SEN/SEN quickly and top off your health with Potions.
-It's all about maxing your damage output and lowering your downtime. Especially with his ability to heal and remove stagger in certain encounters.
Paradigms is a bit harder to remember for me. Just some must haves:
NOEL / SERAH / PET
COM / RAV / RAV - Building Stagger
COM / RAV / COM - Attacking During Stagger
SEN / SEN / SEN - Switch To Before Big Attacks
MED / MED / SEN - Emergency Healing
SYN / SAB / SEN - Buffing and Debuffing.
I'll post if I remember anything else.