Optional objective: Limit time spent in open conflict - 0:15
Optional objective: Limit Chapheau's health loss - 50%
Optional objective: Perform low profile assassinations - 5.
Optional objective: Completed all the constraints in one playthrough.
Start following the angry chef. Your mission will be protecting him from the British soldiers. In order to obtain full synchronization, you need to limit open conflict to 15 seconds, don't let Chapheau lose more than 50% of his health and complete five silent assassinations.
Throughout the whole mission, a dozen or so meters in front of your companion and as soon as you see a soldier, approach him from behind and assassinate with the hidden blade. If you do it fast enough, you should enter an open conflict.
As for bigger groups, start off by eliminating 2-3 enemies with hidden blades and afterwards quickly finish off the others with firearms or quick counterattacks. That way you should be able to keep you companion from participating in any fight.
After reaching your main target, hold down the Assassins Guild button, choose assassination and press the same button again. That way you will order Chapheau to kill William Johnson's partner. The mission will end soon afterwards.