In order to complete this story, you must initially visit Shipwreck Cove to find Jack. In order to do this, you must first conquer a horde of ships led by Luxord (or some bad guy), which, in my opinion, is damn near impossible to do this at Level 1 of your own ship. My direction in this guide is to upgrade your own ship, the Leviathan. If you press the Select button (for The Caribbean map) while captaining your ship, on the left side you should see the level of your ship and Next (which is how many crabs you need to get to the next level), along with other stats such as HP, Firepower, Side Cannons, & Fore Cannons.
My advice for this ship battle is to max out the Leviathan to level 9 (which will give you 9000 HP, as opposed to what you have at level 1, 5000 HP). It's not so difficult to do this if you know where to get lots of crabs. (Crabs are experience points for the Leviathan. You will need a total of 1700 crabs to level up to 9.)
You can gain crabs from battling ships that randomly appear throughout the Caribbean, but for the most part these battles do not gave you ANY crabs (unless they include a ship with red sphere of light, which may give you a handful (12?) of crabs.)
But your best bet is to go exploring and find some islands that you can jump onto and smash some boxes and barrels, in which white crabs will sometimes emerge from. Most of these islands will also have heartless battles, which may provide crabs as well, or maybe they just come from random boxes and barrels that are broken while fighting them, I'm not sure.
I would recommend Exile Island, which is on the lower left side of the map, just northeast of Huddled Isles. Exile Island should already be written on your map before you "discover" it. Just sail your ship close to this isle, by locating it via your map. Then hit Cancel in your control panel by pressing LB. This will stop your ship and allow you to jump off the ship and swim to the shore of Exile Island. Just circle the Isle and smash any boxes you see, looking for crabs to pop out. (Be sure to run around and collect the crabs, as they aren't immediately collected into your inventory like money and MP or experience orbs are. I found that if they aren't being scooped up by me very easily, sometimes a crab will have a hit-target on it and you can hit A and smash it, which should collect it and somehow also collect its friends.) I think you can also get crabs by smashing up some of the palm trees. Look for the trees that get highlighted with a target symbol, as if you can smash them. Then just start smashing the tree over and over again because Sora should sort of climb up the tree and smash its coconuts, which I think somehow turn into crabs. After circling the isle a bit, head inward and you will be attacked by a bunch of heartless, which are fairly easy and fast to kill especially if you're using some Y-abilities. All in all, this island scored me just over 100 crabs each visit, so it's a good place to grind crabs.
Close to Exile Island to the southeast are a few more isles such as Ship's End and Sandbar Isle. These have a good amount of crabs (some under water in their lagoons), but not as much as Exile from my experience.
The best thing about all of these islands for collection is that you can fast travel to them (you may need to find the map for each isle in a treasure chest on the isle to unlock this fast travel though, I'm not sure as I just had fast travel once I visites for a bit of time), which is great because once you're done collecting for a bit, you can warp (Airstep) back to your ship from the isle and fast travel back to Port Royal and save your game so that you don't lose any progress by getting attacked by random ships while travelling between isles. Although, also, Sandbar Isle has its own save point on the sand on the eastern side of the isle (close to a random mountain in the sea), so you could save here as well. (You might need to get the Map:Sandbar Isle treasure to unlock this save point, I'm not sure. That map treasure is in a chest on a rock structure in the center of the main lagoon on Sandbar Isle.
Another good note I have is that if you want to grind away without fast travelling to a save point, you can fast travel to an isle that you just cleared and everything is reset on that Isle so that you can clear it again right away.
Once you max out the Leviathan, conquering Luxord and his horde of ships to unlock Shipwreck Cove should be a breeze now that you have 9000 HP. I found that the ships with green life orb lights were the quickest to kill off, so I tried to knock them off first, to save myself from attack of their cannons. The blue orb ships were close to as quick as the green. Maybe one or two hits for green and three for blue.
As for the rest of popping this achieve, clearly I've done it as I am writing this guide, but I don't really have many tips, except, hang on there, maybe I do. Here I go (beware, heavy spoilers to come):
*** Spoiler - click to reveal ***(After maybe stopping at the nearby Forsaken Isle to save, and of course sailing into Shipwreck Cove first, then after a bunch of cutscene) The first thing you have to do is fight Davy Jones (pirate with tentacles all over his face) for the first time. I found that using Link->Kings' Flare and Simba's A-ability Firaga Roar, which Davy seems to be relatively weak to, to be a wealth of damage to Davy. I used this Link over and over if I had the MP, and he was defeated rather quickly.
The next thing you will have to do is defeat the Kraken as your ship circles it in a funnel of ocean. This is pretty basic. I just hammered away at it with cannon fire, and it succumbed to the cannon fire pretty quickly. It will also be suggested to you by the game to fire at the Flying Dutchan (Davy's ship) using your Y-ability's Raging Cannons ability. This should mean that at this point the Dutchman is approaching to the left (technically behind your ship in the spiraling water) of your ship, so that it is close enough to fire on. I did not have any Y-abilities charged yet at this point, so I just sent some cannons the way of the Dutchman, and this seemed to fend it off enough that it was no longer firing at me. Throughout the whole Kraken fight it seems that nothing else attacks you, so it's pretty brief and not so difficult (this is considering I had a maxed out Leviathan, though).
The next fight is a second battle with Davy, which was pretty basic, like the first, except that I didn't find the Simba Link to work as well, because Davy is jumping between different levels of the ship deck, so I think the Link was confused or just didn't have to ability to fit on small areas of the deck. But, I did find that using the Y-ability that combines Sora with Jack (I don't remember its name, sorry) was particularly strong on Davy, and luckily somhow it was charged up pretty quickly as I used it like three times I think. So stick close to Jack and maybe that will help you charge it.
I think that's the final fight in this story completion. Good luck!