This is an exploit if not a glitch, I'm pretty sure everyone knows it, but if you do not, then you've come to the right place.
Firstly, you must clear Cloud's story once, then travel back through to get the Magic Pot Summonstone, this is crucial, AUTO will not work as well. The reason you need Magic Pot is so you can copy an enemies BRV to yours, the amount of damage you deal to an enemy is what gives you experience.
Next, purchase CPU Level Cap + 100 from the PP Catalog, your enemy needs to be level 100 for this to work.
Next, have the Chocobo Down, Wing and Feather in your accessory slots, to get these, you must get the treasure chest on your Chocobo Play Plan, in the beginning of the game, you are asked to choose a Play Plan. Casual will give you the Chocobo Down along with small EXP boosts, Average will give you the Chocobo Wing with moderate EXP boosts, while the Hardcore plan will give you the Chocobo Feather with extraordinary EXP boosts.
However, to obtain these chocobo items, you must clear the desired amount of battles in a single day before you can get them.
Casual = 15 Battles
Average = 30 Battles
Hardcore = 60 Battles
This may seem hard to do, but if you stick to the game long enough, you'll get addicted enough to do it.
When you have all the Chocobo items, stay on the Hardcore plan until you come across a Gysahl Green (looks like a carrot) with a x5 next to it, a chocobo will notify you if anything changes.
After that, be sure to have purchased the EXP boosts from the PP Catalog, and set the calender to your Special Day, you can reset the calender on the PSP's main menu.
When you have all this, you are ready to fight your opponent, here's a
video to explain the rest. Enjoy!
P.S. I want to clarify something, be sure you have the opponent's Strength at Maximum and his Behavior at Extreme, this helps A LOT!