There will be a long cut-scene with Riku and Captain Hook. Save the game if you want and go to the door. Climb up the ladder. Then climb up the other ladder. You will find that the top is closed off so to the right will be a door. Go through there. Jump down the hole and fight off the heartless. Climb up the ladder and there will be a cut-scene. There will be a treasure chest in the room which contains a Dispel-G. Go to the door and kill the heartless.
Go back down through the door and jump on the cabinet. Next jump in through that open hole. There will be a cut-scene. Go to the door and switch party member to where you have Donald, and Goofy. Do the Green Trinity Jump in that room and climb up the ladder. There will be a cut-scene, and then to be followed soon after by a boss fight.
Cast Aero yourself first then attack. Now when he moves around the floor, you won't be able to hit him, so just run around since he'll slash you from behind once he emerges. When you manage to beat him down to the green bar, he'll summon two other Shadow Soras. Just focus on the original one, since the other 2 have very little HP. You'll win eventually.
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After the battle, examine the hatch on the floor to open it. Drop down the hole and there will be another cut-scene. Open the treasure chest to get a Protega Chain. Go through the door and go back to where you fought Shadow Sora and open the treasure chest containing Puppies 88-90. Go through the door for another cut-scene. You'll obtain the Cura upgrade. Fight off the heartless and there will be another cut-scene. Now you get to fight Captain Hook.
Before the battle begins make sure that you have equipped an accessory that protects against Fire damage. Don't bother going after the little flying ships because you can Dodge Roll away from their attacks. Cast Aero and beat the living hell out of Captain Hook. Also if you get hurt just go behind the ship and heal yourself.
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When the battle is over Sora will learn the ability Ars Arcanum. There will be a cut-scene. You'll be at the Clock Tower. Walk around the corner and there will be a treasure chest containing Puppies 43-45. Talk to Wendy and then go to the clocks. Strike the one that is at 11:45. There will be a cut-scene after you strike the clock. You will obtain Navi-G. There will be another cut-scene. You will also head learn the Summon Tinker Bell. You'll get the key chain Fairy Harp, and then you will at long last learn the shared ability Glide.
The Hercules Cup will be available at the Coliseum. Go back to Traverse Town and talk to Cid. There will be a long cut-scene, and you will obtain the Transform-G from Cid afterwards.