Follow Grant and move while crouching to avoid enemy detection. Once you've reached a shack, press and hold X to get the items on the table.
Right outside that shack is a guard. Throw a rock to the direction marked to your right to lure him away. Continue following Grant to the next hut. Continue follow him then hide in the foliage outside. Throw another rock to lure the two guards away. Continue following Grant and crawl to the trench to reach the checkpoint and a scene.
After the scene, sprint to the forest and continue running until you black out briefly. Continue sprinting and jump across gaps. Don't jump too often as you take damage upon landing. Keep running and make it to the vines. Climb up then continue to a small tunnel. After crawling out, an enemy will jump unto to you. Mash the button to resist and kill him. Continue sprinting to the hanging bridge and watch the next scenes.