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 just to the east of our current location. Sail over here and use the spyglass to identify the target vessel (I found it at coordinates: 764,196). Make your way over and engage it.
It is a decently built frigate, with a fair bit of armour so it can dish out a little damage as well as take it. Use mortars as you approach to drain its health a little and then use the standard combination of chase cannon/heavy shot/broadside to damage it into submission. As you engage the ship, it will cause another pair of frigates nearby to come and attack you. Again, mortars and heavy shots will win the day!
Once the target frigate has been damaged sufficiently to have it incapacitated, approach it and either board and destroy it or fire some of your weapons to sink it if you are in a hurry. Either way, once the ship has been sunk, the mission will be complete.