When you are finally released from your carriage, walk along the path before you and straight up to the gallows. They'll put a bag over your head and continue talking. When they pull the lever to drop you, use your Assassin friend to cut you free (LB/L2).
Achilles will find you and hand you your axe. With axe in hand, chase after Thomas Hickey and stop him before he kills one of Washington's guards. Try to run as straight as possible and only move to dodge so you don't collide with people who will slow you down. When you get to him, kill him.
