Neverland is a world based on the 1953 Disney movie Peter Pan. Despite the world's name, you don't actually get to go to the islands of Neverland. Instead, most of the world is spent on Captain Hook's ship.
The Rescue
When taking the Gummi Ship route to Neverland, the Gummi Ship will come across what looks like a pirate ship. After a long cutscene where Sora is once again reunited with Riku, the party ends up in the Ship Hold. After another cutscene, you'll be able to add Peter Pan to your party. Your new mission will be to find Wendy and Kairi. Exit the area through the door to bump into Shadow Sora, the Heartless Riku introduced earlier. After he leaves, climb up the ladder and enter the door on your right. Go down the ladder here to enter another short battle with Shadow Sora. Now exit the Freezer by climbing up the ladder for a long cutscene. The party locates Wendy and Kairi only for them to be taken away shortly after their arrival. Go through the door and, once again, battle Shadow Sora. Go through the door next to the ladder for another battle with Shadow Sora. Jump up on the shelf to reach the roof above. Where the net is torn you'll be able to jump up to the next floor. Make sure to jump through the opening on the right. In this room, make sure you have Sora, Donald, and Goofy in your party, since you'll need to activate the Trinity mark. Climb up the ladder that's brought down for a cutscene. Sora didn't seem to make it in time, as Riku is leaving with Kairi. He summons an AntiSora Heartless, which serves as your next boss.
AntiSora
- HP: 750
- EXP: 2000
The spells recommended to set to shortcuts are Aero, Cure, and either Thunder or Stop. Thunder allows Sora to attack AntiSora wherever it may be, while Stop can freeze AntiSora for a short period of time. Unlike Sora, AntiSora is unable to use magic, but can instead transform into a flat shadow and move about in that state, as like the basic Shadow Heartless. It can deal a lot of damage if Sora is caught when it leaps back out of the ground. So be sure to keep Sora in motion or use the Dodge Roll ability to help avoid those attacks. After half of its HP is depleted, AntiSora creates replicas of itself to distract you, so use the Scan ability to help speed things up a little bit. But be careful, as those replicas can hit and do the same amount of damage the as the real AntiSora. Once his health is fairly low, he will begin to repeatedly morph into the ground and use the upward sword strike attack for the majority of the fight. This takes nearly a third of your HP and can best be avoided by rolling or countering, this doesn’t guarantee safety however, sometimes you are guaranteed to take the hit. That’s why you always want good healing with you. The fight can and will be impossible as he will sometimes just continue to use the move as you cannot lock onto him and he will not have a hurtbox a fair bit of luck is involved in this fight. Be sure to keep your HP within a tolerable level - heal when necessary. The Guard ability is particually useful if it is combined with the Counter Attack ability in this battle, as you can deflect some of AntiSora's attacks.
After the battle, go to where AntiSora disappeared into the ground and Examine a section of the floor. Here will be a trap door, which you can drop through for a cutscene. At this point, Peter Pan will leave your party to help Wendy. The rest is up to Donald, Goofy, and Sora. Exit through the door and then go through the door on the right to end up in the place you were before the battle with AntiSora. Climb up the ladder and exit through the door in front of the trap door for a cutscene.
Captain Hook
After the cutscene, Peter Pan will return as an optional party member and Sora will have the ability to fly. Sora also gains information on the whereabouts of Riku - Captain Hook tells Sora that Riku went to Hollow Bastion in search of Maleficent and, unfortunately for Sora, he took Kairi with him. After the cutscene, you'll have to defeat the Heartless left to you by Smee and Captain Hook. The controls for flying are the same as swimming - 
to ascend and 
to descend. After you get used to flying and finish the battle with the Heartless, a cutscene will show Captain Hook coming out of the cabin to fight the party. Also when you finish fighting the heartless, any dead characters would be brought back to life, but only the dead would have any health or MP regeneration, so make sure you have plenty of potions and ethers.
- HP: 900
- EXP: 3400
If you are flying when the battle starts, descend to the ground and land on the deck. Lock onto Captain Hook and make sure not to lose him. If you're flying in the air, Hook won't stay in one place, so it would be wise to keep your feet planted on the ground. Ignore the Battleship Heartless, because even if you destroy one, another one will take its place. What would be a good strategy is when your HP is at critical and Hook and the Heartless are closing in on you. Fly from the boat and hope you can heal in time until the Battleships arrive. By this point you should have just obtained Cura.
Fight Captain Hook head-on, and make sure that you have Aero cast while doing so. If your HP meter gets too low, fly away and heal yourself before continuing. If you can, try evading Hook's rapier, or guarding against it - for it can deal substantial damage.
If you cast Fira on Captain Hook, his pants will catch fire and he will run around the deck. If he runs into you while on fire, it can damage you, so fly into the air to protect yourself. Also, if you use a combo on him and knock him into the air, he has a chance of falling into the water - after which, he will jump up and run helter-skelter (for fear of the crocodile). When this happens, you have a very good opportunity of attacking him because he has let his guard down. Hook happens to be immune to Thunder, so don't bother using it. If you get too far for Hook to reach you, he will throw present-bombs, similar to the one he gave to Peter Pan. With a good balance of Cura and Aero, you should be successful. After winning the fight, you will gain Ansem's Report 9 and the Ars Arcanum ability.
The Keyhole
After the battle and another cutscene, you'll end up on London's clock tower, Big Ben. Here, all of the clock's hands will be set to 12:00 except for one, which is 12:45. Hit the hands with the Keyblade to make it 12:00, and the Keyhole will be revealed. Afterward, you'll gain a new summon, Tinker Bell, and you'll be free to leave the world.