Defeating the mercenary with flame thrower ends the battle in the village. Now you need to get to Acropolis. The bridge to the building is destroyed in two spots. You can cross the first hole without any problems, you simply need to walk around it. The other one will require you to be smart. Stand in front of the hole, and take several steps back to gain speed. Remember that you sprint by holding down the left analog stick. Sprint towards the chasm and at the last possible moment, take a leap and use the hatchet. If you fail, Lara drops into water and you will have to try again.