When you reach the docks where the Aquila is tied up in place of the usual interaction with the Harbormaster you actually flag the next mission for the story...
As Connnor has already outlined the plan to Lafayette you should have a general idea of what is about to happen, but you need to know that the optional objectives for this are to destroy ships using only one broadside (x3) and destroy the frigates by targeting and firing on their powder stores (x2). After the sea battle stage, you will also need to perform counter kills enemies (x5). This sounds a lot harder than it really is – the Aquila should have been fully upgraded long ago, you should be very well versed in handling and fighting her, and thanks to several of the previous naval/Privateer missions, you should also be pretty handy at exposing weak spots, targeting, and shooting them!
So flag the quest and the CS plays out, then you need to go for the first optional objective and destroy at least three of the gunboats with a single broadside. I suggest that you use grapeshot and that you remember to pull and release rather than holding down the trigger to fire. The reason for that is because the longer you hold the trigger down before releasing it, the more focused the aim is, and in this case we want the shot to go out as wide as possible so that it succeeds in taking down three or more of the smaller boats.
The Arrival of the Frigates
Once you have taken out the flotilla of smaller boats a trio of Frigates will appear, and to meet with the optional objectives you must destroy TWO of them by exposing their weak spot (gunpowder store) and targeting it. The good news is that one of the trio already has that spot exposed so you can charge right in and blow it to smithereens!
Technically you only need to destroy one more, so there is a margin for error, but the best approach is for you to change over to chainshot and cripple both of the Frigates so that you can use the ramming-technique to expose their weak spots. Then you simply target those with your Swivels and blow them away, fulfilling the second optional objective.
Boarding the Frigate
The next stage of the battle has you boarding a Frigate and fighting on the deck. Killing the Captain will end the battle, so ignore them for the moment since you need to engage the crew in order to complete at least 5 counterkills. A counterkill is simply hitting B to block and then X to counter, thus killing the bugger, and I suggest that you use your Hidden Blade for that move, as it is almost always faster than the animation for the other weapons. For this objective you have to remember NOT to chain your attacks! Your goal is to do at least five counterkills, not chained kills.
Once you have completed that last optional objective, go ahead and kill the Captain to end the battle, and then you will need to bail out of there because you shoot the exposed powder barrels and the ship is about to go kerblewie! Your crew is impressed, and as the closing CS plays out the French fleet finally arrives!
Connor explains the plan to the French Admiral and then you get the summation of the mission success. Well done you! Another mission completed with full-synchronization!
After the previous mission ends your ship has docked in New York City, and you make ready for the next phase of the plan. For this mission there are again three optional objectives, with the first two connected together as before. They are to reach the signal tower within the three-minutes allotted to you, and for you to remain undetected all the way to when you light the signal fire. In addition to that, you also have to limit health loss to 50% for the combat portion of the mission.
After you flag the mission you enter the tunnels of the Underground it is a very short path to the meeting place - just follow the markers - and then you get a brief CS and you emerge in the fort, inside of a well. A guard is leaning against the well, so go ahead and pull him into it to kill him, then emerge and head straight to the alley and down it, hiding behind the fence on the left at the end until the patrolling pair of guards pass, then quickly cross and to the left, turning right into the next alley!
Halfway down this alley there is a wooden fence on the right – either slide under or climb over and go to the far end, where you will find another fence at the corner with a ladder going up to the roof of the building on your left. Climb up and kill the guard on the roof, then run and jump to the opposite roof, then jump down to the ground and run to the corner ahead, peaking around. Try to kill the guard as best you can who is patrolling here before he goes into full-blown discovery mode (a red triangle will not blow the optional objective).
Run to the tower and begin climbing it, ignoring any red triangles you see, get to the top and light the signal fire, triggering a CS in which you jump down but the shelling is too close for comfort and you end up stunned.
Basically at this point all you have to do is stumble forward until you trigger the next CS, you stumble through a building and end up in a cave-like tunnel in one of the walls. When you emerge from that you are confronted by your father. It is at this point that the second phase of the mission begins, and where you have to limit damage to yourself.
This is a boss battle, and the thing about this battle is you CAN NOT attack him directly. Do that and you get hurt. Do it more than once and you blow the optional objective. This is a fight in which you can ONLY use environmental objects to damage him, focusing your entire engagement with him as a defensive battle in which all that you need to do is move next to a new object and then block/parry his attack twice to trigger the animation.
You should only need to throw him into three or four objects before it triggers the action-CS and then you are prompted to deliver the coup-de-grace. I did not see that coming!
At this point you get the synchronization summary and you unlock the Achievement “Difficult End” (20G) Complete Sequence 11. You likely have mixed emotions about this – I know I did – but Achilles explained why this had to happen, so take it in stride. It is not like Connor had a relationship with the man, right? After the summary plays you get a new CS in which Connor prepares for his next mission and then the game immediately goes into Sequence 12 (you are not given the option of not starting its first mission).