After a visit to the inn, head out to meet with the Indian woman. The proper mission will begin there.
Optional objective: Kill militia without triggering open conflict - 2.
Your first task will be killing a soldier marked with a red dot. You can rush onto him at once and take out the whole camp with Indian help, but you should complete the optional objective beforehand. It consists of eliminating two enemies without an open conflict breaking out.
In order to complete it, go round the soldiers form the right and hide in the nearest pile of leaves. Beside it there's a guard who you can assassinate. Do it when the marked enemy walks away to a safe distance.
After executing him, sneak to the pile of leaves a couple steps further. From there you will be able to eliminate another enemy who's patrolling the edge of the camp.
After killing him, attack the others without worrying about getting detected.
That way you will obtain an uniform and will be able to safely ride to Braddock, marked on the map.
Optional objective: Destroy powder carts - 3.
Optional objective: Completed all the constraints in one playthrough.
After a short animation, the man will start to run. Chase him by holding down the free run and jump buttons.
Your additional targets are the gunpowder carts placed nearby the road. To destroy them, you will have to press and release the secondary attack button when nearby them. Remember to quickly reload the weapon between carts by slowing down for a bit (let go of the jump button) and press the shoot button). Your character will do everything automatically while riding the horse.
As you catch up with Braddock, yet another chase will begin, though this time on foot. Get a couple meters from the enemy and kill him with a fast pistol shot. That way you will end the mission.
The whole sequence will end after you visit the inn marked on the map.