Mister Walpole, I presume?
During this memory you are introduced to the main Templars, as well as obtaining a pistol and hidden blades. Time for some exploits.
First off you can remove Edward from the scene with Woodes Rogers and Julien du Casse by being in a climbing position. There is a tree that leads to a railing. Walk up it and wiggle as close as you can off the edge. In the rare event you get close enough you can grasp on to it. Then very carefully move along it until you get the scene to start. There's something else you need to know. If you are in a climbing position where your hands are close together it won't remove you from the scene. You don't see it in the video, but I actually move back to the right when the scene is starting. What follows is an introduction to an invisible Edward and a floating pistol.
Early Deaths
Not bad you can kill the main Templars in the same memory of their acquaintance. The opportunity is right after Woodes, Julien, and you are sworn into the Templar order. By tapping the assassinate button in high profile during the end of the scene you get Woodes and Julien in a double assassination (in low profile you just get Woodes). The strange thing is for Edward the killing animation gets cancelled, giving the illusion they just die suddenly, although dying people don't generally just throw themselves onto a table/the ground. When the time comes for one of them to speak no dialogue is audible for the rest of the conversation. The kill/kiils also cause a glitch with the following scene not starting, preventing you form progressing any further in the game.
You can also get Torres this way by moving the left analog stick to the upper left while tapping the assassinate button on high profile. As for the last guy, El Tiburon, he's either out of reach or invincible to assassinations.
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Sequence 2 memory 4.
A Man They Call the Sage
At the beginning of the memory you catch glimpses of assassins running around. So far I've seen five, which all can be killed in one take. They're everywhere, in the streets, on rooftops, even in haystacks. Some are scripted to appear at certain times, while others are affected by being within a certain area of them. And they disappear at a certain point, so killing them has no effect on the mission.
For the mission itself you protect Torres from assassin attacks. The rooftop archers are the only ones who can do damage to him, so if you take them out fast enough there are no worries about him losing any health.
Early Death
The last part of the mission has you chasing after the Sage. The game developers didn't want you to be able to kill him, and so desynched you if he was killed or incapacitated. However... there is an exception. A ground stomp, which actually seems to start the scene.
The way I did it was plant barrels from the nearby places (one in a restricted area and two in a building) and shot them after the scene to knock him down. It seems the barrels will kill him if he's too close when they blow up. A ground knockout with fists or hidden blades is recorded as an incapacitation in the stats, which is a way of assassinating targets, so I'd count it as an Early Death.
A ground kill with swords desynchs you. Also if you perform an air tackle you have time to perform a ground stomp (not enough time with a regular tackle), so using barrels isn't necessary, although it adds some THB flair. Since it's so easy I expect other people may have discovered this, although I have yet to see anyone else document it. Another thing to note is if he's knocked down and you get near him the scene starts even if he's already gotten back up.