If you stray into the sea area below the Pirate Outpost, you may be attacked by Captain Crawfish.
In order to beat him, you need a ship as powerful as his: the Phoenix Warbird. You will have to buy smaller ships as you can afford them, so that you can earn doubloons more quickly. When you have 500,000 saved up, you can borrow another 500,000 from the Golden Harbor Bank and buy the Warbird. Once you have this most powerful of ships, you can attempt to sink Captain Crawfish. If you succeed, you can get the location of the Buried Treasure from the Governor.
When you have traded and salvaged enough to buy larger ships, and trade up to the Phoenix Warbird, you will have a chance to defeat Captain Crawfish. You should also have the Shipwright and the Cannoneer.
Sailing near the hidden island Skullduggery will usually bring out Captain Crawfish quickly. Pound him with your cannons and watch your own health. One way to reduce him is to sail ahead and aim your cannons almost straight up : the shots will land on him when he follows you. When his health goes to zero, he doesn't sink like the other ships. He escapes and sails away.
Once he is gone, the Governor will give you the bone shovel and location of the buried treasure on Skullduggery. Sail there and dig it up.
You will encounter Captain Crawfish if you sail in the waters around the new small island, Skullduggery. You will need a powerful ship (the Phoenix Warbird) to outlast him, and he runs off when defeated. Once you have the five pieces of the map, and chase off Captain Crawfish, sail back to Fort Ridley and the Governor will give you the bone shovel, and the location of the Buried Treasure on the hidden island. Go there and dig it up.
You chase him off. Other pirates get sunk, but he just runs off when you beat him. You need the largest ship, the Phoenix Warbird, and you need the shipwright and cannoneer as crew.
Nothing until the very end of the game. Once you have all five pieces of the map, put them together to reveal the 6th island ("little Skullduggery"). You can go there but there is nothing to do. After you chase off Captain Crawfish in battle, the Governor at Fort Ridley will give you the location card for the Buried Treasure, and a bone shovel to dig with. Sail to Skullduggery and dig up the treasure.
There is no way to, and no reason to, give the map to him. When you have all five sections, put them together to reveal the 6th island, Skullduggery, located near the Pirate Outpost. Not only does it appear on the map, but you can now actually sail to it. Once you chase Captain Crawfish away (in battle, with a big ship), the Governor will give you a bone shovel and the location of the Buried Treasure on Skullduggery. Go there and dig it up.
You have to get a lot of doubloons to get the Phonix Warbird by beating other ships so you can get a lot of doubloons from them. When you have about 500,000 you can loan another 500,000 from the bank and buy the phonix Warbird and to beat him fast you chase him around skullduggery island and then when your on the side and captain crawfish is on the other and you are anchored then you have to shoot him repeatedly so you can beat him.
Normally, only the most powerful ship, the Phoenix Warbird (using the Cannoneer) can defeat Captain Crawfish. There is a tiny chance of beating him with the Steaming Fury ironclad. The problem is that he will stay close to the Pirate Outpost and simply dock there to repair his damage (as you can). You would need to be very lucky, so the usual plan is to fork out the million doubloons for the Phoenix (and hire the Cannoneer). *If you are attacked by Captain Crawfish, one way to hit him is to let him chase you. If you fire cannon shots almost "straight up" (aimed above your own ship), they will fall onto him as he pursues you.
Once you have all five pieces of the Treasure Map, the 6th island, Skullduggery, appears on the map. When you acquire a powerful ship, and scare off Captain Crawfish, the Governor will give you the Treasure location and a bone shovel to dig it up. (see related question)
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