If he smacks or throws you and you take damage...

...get up as fast as you can and start running around the edge of the arena.

Try to stay ahead of the stalker—on the opposite side of the arena if possible—and keep moving. If you do this, he should just follow and not try to swing at you. Keep running and evading until Lara's health regenerates. Just be sure to avoid the edges with the flaming debris, which will only make things worse, and don't let him corner you or he will hit you again.

When you've done sufficient damage to the stalker—which varies depending on the difficulty setting—he'll sink to the ground, dropping his club momentarily, and you'll see the Melee icon above his head. Move in close and press the Melee button.

As Lara swings her axe, press Melee again in time with the on-screen prompt...

...to smack him in the face. This hurts him but also pisses him off. A lot.

As he stands up, you regain control, and a checkpoint registers. Now, along with the stalker, you must also deal with 3 Oni archers, who crawl up out of the chasm. Take them out as quickly as you can, while also avoiding the big guy.

Here I like to switch to the pistol or rifle, move in close to one archer and let him have it.

Then, when the Melee icon appears above him, press the Melee button...

...to use one of your special finishing moves.

Occasionally, if Lara is standing near one of the archers, the stalker will swing his club and take out the archer by mistake. But don't count on this. (Sorry I wasn't able to get a screenshot of this.)