Once the mission begins, hop in the Jackdaw and sail over to the location on the map marked by the green objective marker. As you arrive a short cut-scene will play.
When you regain control, we’ll see a brig and four gunships sail past. Quickly use the mortar when you regain control to damage the gunship (and potentially take out a gunship or two) before it gets in too close. Following that, move in to engage them in battle using the usual circling and broadside/heavy shot tactics to deal with the threats.
Note that due to the narrow section of the channel here, a well-placed broadside can easily damage or sink 2-3 of the gunships at once. Try to focus on sinking the gunships first before turning your attention to the brig.
Once the brig has been damaged sufficiently to have it incapacitated, approach it and begin boarding. During boarding, we’ll have to kill 10 of the crew members. Doing so will complete the contract.