Begin the mission be leaving the manor and speaking with Achilles who's waiting on the carriage. Together with him you will head to Boston to buy supplies.
Follow your companion, enter the first shop and buy the needed materials.
Afterwards return to your master and you will witness a demonstration.
You will receive a mission of following the mysterious man. While making sure he doesn't notice you, follow him to the roof and wait for the marker to change from orange to red. That will mean you have to kill the shooter as fast as possible.
Optional objective: Escape within the given time - 1:20
Soon enough you will be have to escape a chase. For that, leave the red zone marked on the map and find a hay stack or a well in which you can hide. You can't be seen by any soldier when entering your hideout. If you run within 1:20 minutes, you will gain full synchronization.