Defeated a powerful enemy on equal terms.
The powerful monster you have to find is called Raspatil. It's very rare and does only spawn in Oerba 400AF at the white beach. To reach this location enter the blue gate in augusta tower 49th floor (requires wild artefact) and travel to Oerba 300AF. Solve all paradoxes in Oerba 300AF (there is an invisible one at a staircase near the beach, use moogle hunt to make the paradox visible) and go through the blue gate (requires wild artefact) to reach Oerba 400AF. Run up and down the beach or keep running in circles. Raspatil spawns about once every 20 minutes (when you keep moving all the time).

Again, the appearance of Raspatil is completely random and based on luck! The shown area is the only location to find him.

You will have to play on normal difficulty when going for the trophy / achievement. Easy won't count! Make sure all your characters are maxed out and you have high level monsters. There should be at least a synergist monster in your team that can cast Bravega and Faithga. You won't stand a chance otherwise! The fight gets increasingly harder the longer it takes. Do always cast negative spells with the help of a saboteur to weaken Raspatil (especially before you stagger him). Once staggered bring up his damage over 900% and switch to a pure commando paradigm to cause as much damage as possible in a short amount of time. Don't ignore the small monsters he spawns! Take at least some of them out. He absorbs them after a while to power up his attacks. At some point you will instantly get killed.
Most important monster for this fight is the Yakshini (best synergist). Use his feral link in tricky situations, it's a pure life safer. You can find and capture Yakshini in Vile Peaks 10AF.