This battle is a magic battle. To get the most of you and your party's MP, de-equip all of their abilities that comsume MP, except MP Gift, and use all of the MP restoring abilities, such as MP Rage, as possible. Your party should be Goofy and Peter Pan, because Pete is required to talk to Tinkerbell, and Goofy is needed for his MP Gift, which turns itself into unlimited MP.

To stop his Doom, simply fly by the Clock Tower (any face) and cast Stop/Stopra; I highly recommend that you make it one of your shortcuts, and I found that Square works best for me.

Depending on the color of his ball(s), you can either use Thunder>yellow, Ice>blue, Fire>red, or if it is clear (which is your only, if not major attacking option), simply bash away with the Keyblade. This one may take a few more than a single try, but as a reward, your Stop/Stropra magic is upgraded instantly to Stopga.