How do you get high up Puzzle Pieces
Solution 1:
For some of those high up, hard to get ones, you will need to level up Valor, and Master forms to level 7 to get High Jump 3 and Aerial Dodge 3. In addition, there will be some that you won't be able to grab until you get Final Form leveled up and have Glide (at least level 1), but not many. The most notable two I can think of that you need glide for are in Halloween Town (by Curly Hill) and Land of Dragons (Throne Room). You won't be able to level them up to max until you get the Final form though, and you don't get that until
after you fight Roxas in the World that Never Was
There are a few that you can get before that though, even though it is a lot easier to do so after leveling things up. The one in Hallow Bastion you can get earlier if you extend your jump a bit by attacking. And there are one or two in Land of Dragons you can get boosted into by an enemy attack if you time it just right.
Solution 2:
For the annoying one on the boat, the way I done it was by standing right infront of the wheel as there is a little bit of surface to stand on, then use aerial dodge (lvl 2) to either side of the puzzle to avoid the rope, and use glide to secure getting it :)
Solution 3:
After the gummy ship is forced back to HB, you can talk to Duck Mc Scrooge (he is in front of the giant fridge shop) to borrow his skateboard. Grind along the railing and jump off while doing 360s to get over to it. It will take a few tries.