Yeah, you log on to the website, pick your save file and hit the Character Booster button. At which point, everyone becomes level 99 and you get 49m gil. Also, you can't reverse it.
Sounds kind of disappointing. If you wanted to get to the 99 999 999 gil achievement easily, it might be something you would want to do, though.
The final boss's stats changes depending on the stats of your party. So for every character at level 99, he gets an HP boost of 30K, +2 ATK, +5 MAG, +16 MDEF, +20 or so PDEF. Every time you kill the previous boss's head, the final boss's HP will be reduced by 100. There's a limit on this and I forgot what it was.
So if you take all of that stat addition into consideration, the final boss's max stats are: 400K HP, 246 ATK, 140 MAG, 308 MDEF, and 260 PDEF. DEX and EVA aren't affected, I don't think.
Edit: I'll say that it is not hard to fight him at Lv 99, though.
I almost want to say to try to snag a 1998 version because it's much easier to mod/patch, but since this and the PSN versions of FFVII are more easily accessible, you could try those too.