Disclaimer: Not my game, controller, leet skillz, camera or Youtube Account. I just found this vid.
YouTube - KH2FM ES Battle ---- LV1 No Damage
That guy defeats the ES at Level 1 with the Holy Pumpkin. It seems that by maintaining a certain distance to the ES, you can determine his attacks. In the first half of the fight, nearly all his attacks are gliding around, followed by his aerial slashfest. Later, he always uses his Limit Move. That guy simply dodges, guards and slashes away at him.
So, it is indeed possible to beat the ES with Exp 0. Just looks kinda boring to me :P
Edit: Oh yeah, and this is the guy that defeated all Org XIII members and the ES with no damage at LV 99 previously.
Edit 2: Okay, will all of you please accept that this guy has defeated the ES at Level 1 without any cheats?
First, he is indeed LV 1. He even shows this at the end of the video. He also shows that he is in Critical Mode.
Second, yes, he is LV 1 without using a cheat. There is an ability called EXP 0 in Critical Mode that stops you from getting any experience points.
Third, his health, forms and abilities are not determined by his level! You get skills and health points for beating special encounters like bosses, and you don't need regular experience points to level up forms!
Fourth, he doesn't do "too much damage". The ES has very low defense, but he has some kind of invisble barrier that prevents most damage until you knock it down. This can easily be seen as the first in a row of two combos always does very little damage, while the second one does a lot more. If you still think the damage is too high for LV 1, check his LV 99 video, he does 5 times more there. Not. High. Defense.
Edit 3: And I thought all had been said... You have EXP 0 at the very beginning of the game. You do not need the Mushroom keyblade, although it has this ability too.