After the cutscene Peter Pan can join your party. Now exit the room, once again there are a lot of Heartless in this world so take them all out. You will also see a Shadow Sora that will float around in some areas, defeat these as well, because they are jut plain annoying because they just dance there.
Then climb up the ladder and enter the room that is opposite to the room with the Yellow Trinity in front of it. Once inside, jump down the hole in the floor. Climb up the other ladder into a new room. In this new room, hop into the shelves and jump through one of the holes in the ceiling. Use the Green Trinity to enable to reach a boss. Best to save your progress first though.
Boss: Shadow Sora
This is a little tricky. Shadow Sora is quick and can deal lethal damage. Using Dodge Roll is a good idea. He can sink into the ground and appear behind you, it is a good idea that you Dodge Roll at this moment.
Also when you see Shadow Sora spilt up into 3 separate Shadow Soras, use Scan so you can see which one is the real one because the fake ones have very little HP. When you beat him, you will get a Cure Magic Upgrade and Ravens Claw.
Examine the trap door in the room and Peter will ditch you. Then save and go back to the Captains Room and go through The door to the Deck. Press jump twice to start flying. Destroy the Heartless and get ready, then go through the door and go through the door in the Captain’s Room to go to the deck.
Boss: Captain Hook
Flying for this battle is a good idea. Avoid his sword attacks and his present bombs he throws at you. Be careful of the Heartless that he summons to his aide. He is really weak to Fire Magic as well. Don’t get anywhere near the presents he throws. Also, his slash attacks can do some pretty big damage, so try not to get in the way to too many okay? After the battle you will be on the Clock Tower.
Fly to the side of the Clock Tower that has the wrong time. It will show 11:45 instead of 12:00. So lock onto the hand it hit it to fix the time. Then, after the cutscene, go to the Save Point that is on the top of the Clock Tower, and go back to the Gummi Ship.
Chip and Dale will tell you that there is another tournament being held at the Coliseum. But don’t go just yet. First, you should go to Traverse Town and get Cid to install the new Gummi Piece. Once you have done that, head for Olympus.