The Dartmoor is a Man-of-War ship that you are sent to hunt down.
A Man-of-War is the most difficult of all ship enemies for you to deal with. These have cannons and lots of them. They are also the most durable ship that you will encounter in the game.
It is capable of firing broadsides from its, Port, Starboard and Stern. This makes it only safe to approach from the bow. Keep that in mind. Still, broadsides are your best bet to take out this threat.
If you want to expose a Man-of-War's powder store then the best thing you can do is use chain shot to bring down its mast and limit its speed. After that, ram the bow. More often than not this will expose the store to swivel fire. The use of Heat Shot is also recommended against them.