Hmm... in the first KH it would be impossible, unless you've got really fast fingers. In KH2, it would be, and then on your battle report at the end of the game it would say, "Times Party was Healed(or something to that effect)" Then below it a big fat ZERO. Sorry for any spoilers.
Though it would be hard, seeing as you can't use items in the air. Then if youre about to die in mid-air and whatever you're fighting catches you, you're dead meat.
I would say Xaldin. Out of all the tries I fought him(WITH King Mikey as well) I never beat him. My friend did. Demyx, on the other hand...
He may seem like a wimp, but he's not. I haven't counted how many times I lost, but I lost. A LOT. What got me the fact that Donald a) is no help at all. b) happens to have his Auto-Limit equipped. So I'm dead and beeping, Donald has half-health and FULL HP, and he heals himself. I die, 'nuff said.
Eh, I would say Lionheart in the first game, Bond of Flame in the second, and since I never bothered to get Ultima in either games, I don't really know.
Kingdom Hearts is the heart of all worlds, as all the people say. It confuses a lot of people, so don't worry. Kingdom Hearts can make Nobodies whole, which was the Organization's sole purpose. Hope this clarifies.