After beginning the contract, we’ll first need to go and find the ship that we need to destroy. If you look at your map, you’ll see that there is a large, green investigation zone to the southwest. Sail over here and pull out your spyglass to identify the target ship (I found it at co-ordinates: 255,425).
As we approach, the ship will not become hostile until we attack, so take the opportunity to get in very close and use the usual heavy shot/broadside combination to dish out some hefty straight-up damage. Afterwards continue to whittle away its health until it is ready to board. At this point, you should focus on destroying the gunboat that was escorting the target (if you haven’t already).
Once the target vessel has been damaged sufficiently to have it incapacitated, approach it and begin boarding. During boarding, we’ll have to kill 15 of the hostile ship’s crew members and 2 powder stores on the deck. Doing so will complete the contract.