After bringing Haytham to your boat, use it to follow after Church. You'll have to navigate some tricky areas before you start getting to some open water. Off to the right, you'll find an abandoned ship. When you go to investigate, you'll be attacked. Follow the ship that attacked you and it will lead you to some tricky areas.
You'll have to navigate a bunch of rocky islands in this section but it won't be easy as the wind never gives you a simple line towards the enemy ship and you'll have frequent rogue winds trying to push you into the rocks. Keep after the ship and try not to take too much damage before catching up with the ship. You need to be both fast and careful to meet both constraints.
Eventually, the enemy will lead you to a large open area but there will be quite a few ships out there waiting for you. You want to subdue the large Man-Of-War ship but you don't want to sink it so focus first on the smaller ships around it. Most of these ships can be taken down with a single broadside (sometimes two at once) or at most two swivel shots. Keep moving and take out the escorts. When you have, change ammo as you would normally change tools to equip the chains you need. Get as close to the enemy as you can before releasing your shot. It's best if you can come right up alongside the enemy. It may take a couple of shots to bring down the masts but as long as you are close enough, you'll get it.
With the masts down, you'll board the enemy ship for combat. There are three officers marked on the upper decks with red markers. Find them and either assassinate them or kill them in combat by disarming them. If you can't seem to find one of them, kill the ones you can find first and the other will likely come to you. When you kill all three of the officers on the deck, this section will end. Be sure to get a three kill chain before doing so to make sure you meet the constraint. It is best to do this with the regular enemies on the deck. Just remember that to change your target and attack a new target just after delivering the killing blow.
When you've killed the three officers, you'll go below deck. Go through the holds of the ship to the end and find Haytham with Church.
