This sequence is also shown in a gameplay video.
Try to keep moving as much as possible without leaping off the edge, and keep Lara's gun(s) drawn. She can jump much higher, as well as perform evasive rolls, when she's holding a weapon. (You may need to holster them momentarily to fix the camera angle if it becomes skewed.)
Soon he'll run off to the other side of the ledge. Keep repeating these same tactics. You'll see his health bar—the orange one at the top right—diminish each time you hurt him. It doesn't take too long to kill him at close range, provided you can manage to keep Lara alive.
If you run out of ammo for your more powerful weapon, go ahead and shoot with pistols even if the targeting reticle is gray. You'll still hit some of the time. Then try and get closer so you can do more damage. Or, switch to one of the alternate strategies at that time.