Vane is not mentally well. He is using the Grenades and flintlocks he's found to attack Edward. Wait for Vane to fire then dart forward to the next section of wall. Go over to the right-hand edge of it. Wait for Vane to fire his next shot and start throwing the grenade to duck over to the next wall ahead of you. Hide here and wait at the left-hand corner. Once again, dart forward toward Vane to the wall ahead on the left. Go to its left-hand edge and wait again. After the next shot, run over to the left. Go behind the wall and start up the bank there. Follow it over to the right. Stop before crossing the log in front of you because Vane has left an ignited Powder Keg on it. Wait for it to explode.
You still need to keep after Vane. Run down the broken log and jump over to the second part of it to your right. Turn to the North after that and start on up the path found there. Climb on up the next tree and jump over to the walkway. Head through the village using the walkways. There is a jaguar in the area below so be careful if you fall.
When you make it through to the second explosive that Vane's put in your way, move carefully. There is a third ahead of you on the far side of the bridge. Go near the end of the bridge and look to the left to find some trees that will let you cut around it. Follow them to the ruins ahead on the right. Head on through them to the East. Go on up the stairs there. Follow them to reach the Temple that Vane is using as his base.
Once again, you need to approach him but this time, Edward will not be gentle. Go forward and to the right. Repeat this to get closer to the temple. When you get to the right-hand side of the temple, go around to the back of the temple. Go to the right-hand portion of the temple, behind the off-shoot section. user that to start the climb up the temple. Make your way to the Viewpoint above Vane. Just get there and air assassinate Vane to be done with him.