This trophy will likely happen by a chance critical hit towards the end of the game, but if that doesn't happen...
Towards the end of the game, pick an enemy weaker than you, and attack from the front to avoid Chariot's instant kill move. Equip your best weapons, and choose a character/persona with either the charge or concentrate ability.
Enter battle, buff that character's attack, debuff the enemy's defense, use charge or concentrate, and then follow up with a physical attack or your strongest magic attack (respectively). Towards the end of the game, that should easily top 999.
OR
If that still doesn't work, make sure to max out the Strength Confidant, and obtain the late game personas (such as Michael, Lucifer, or the component parts of Santaneal), which likely approach or reach level 99 with Confidant boosts. Register the personas, beat the game, and start NG+
As soon as you can, hit the registry, pull out an end game persona, equip the main character's best gear, and follow the above plan. The main character will essentially have level 90+ stats from his persona, and end game gear going up against the weakest enemies in the game.