Once you’ve cleared Echo Lake Lumber and completed the quest “Turn Back the Fog”, fast-travel to the new settlement and this quest will automatically start. (I've read from other sources that the quest might be given by settlers from other settlements) Talk to one of the settlers to get more information about this quest and to get and additional optional objective of consulting Old Longfellow.
After consulting Old Longfellow he'll even offer to come with you as you hunt down the beast. The next problem is finding the Shipbreaker's signal. The location where you can get this signal is randomized and once it appears in your Pip-Boy's radio, you need to track it fast. The percentage of the signal strength will appear in the upper left screen and you have to head to the direction where the signal strength increases.
Upon finding the source of the signal, you should find this unique Fog Crawler. Saving first before getting its attention is recommended. Also, sneaking and landing an easy critical should be a good headstart but be warned, this creature is possibly the nastiest and toughest fog creature the island can throw at you. A power armor can help you soak up most of its damage but frequent stimpak usage might be needed. If you have devastating weapons like a MIRV launcher or an ordinary Fat-Man, expect this fight to be a lot quicker.
After destroying the Shipbreaker, don't forget to get the valuable loot it has then talk to Old Longfellow again. You'll receive the unique harpoon gun "Skipper's Last Stand" as a bonus as well.
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