Have you completely beaten the Lunar Ruins? ie, have you completed every character's trial, and gotten every treasure both in the trials and on all the random floors? Some trials, especially Cecil's, require you to complete them multiple times to get every possible item.

And speaking of items, have you gotten every item in the game, including all the other rare drops besides the summons and Pink Tail? The Fat Chocobo inventory was increased in the PSP version, so you can now hold every item in the game, with room to spare.

Have you done all the other little side-quests, like getting the Knife, Excalibur, fighting and acquiring all the other summons, and exploring the wonders of the Developer's Room?

If you've done all that, you've probably done everything you can do in FFIV.

What about levels? Is everyone level 99? Are you a bad enough dude to go for perfect post-70 stat gains on every character (please say no)?