Taken from the guide on Gamespot by Jet2x5:
//FAIRYTALE PIRATE - CAPTAIN HOOK\\
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ATTACKS
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Swash Buckling: Captain Hook just normally attacks with his sword.
Surprise: He throws an exploding present at Sora.
Sleight - Rush & Present: He launches numerous exploding presents at
Sora.
Sleight - Combo & Present: He does a long string of attacks on Sora and knocks
him in the air. When he lands, he drops a ring of
exploding presents on him.
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STRATEGY
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Captain Hook is pretty tough. Though he's tough, he is simple to beat. Just
use combos, summons, magic spell stocks like Firaga and Thundaga, stock summons
like three Clouds to make Omnislash, and Sleights like three different type of
Keyblade attack cards to make a Blitz.
Hook has a little pinch of a second health bar, so he's easy to beat. The only
main worry is his Combo & Present move, and the boat rocking back and forth. Do
what I said and he should be done for. After that's over, grab his card and
if you leveled up, choose Sleight. If you're lucky, then you'll probably learn
Ars Arcanum.