When first icon appears on screen, aim at Mathias and press the Fire button as he trudges toward you. Whether or not you hit him, he knocks the gun out of Lara's hand and punches her in the face.
She grabs her axe and starts to take a swing. As she does, press Melee in time with the on-screen prompt. If your timing is good, Lara hits Mathias in the back as he tackles her.
Once he has her pinned on the ground, she spots her pistol on his belt, but before she can grab it, he shoves her down and tries to choke her with the climbing axe.
To get free, you must first tap Interact repeatedly to push him away.
If you succeed, Lara grabs the pistol and fires once. The shot wings Mathias, and he scrambles away clutching his shoulder.
Lara reaches for her the gun she dropped earlier and stands up holding both pistols.
Aim at Mathias, and when the button prompts appear on screen, alternate pressing Primary and Alternate Fire (LT/RT on the Xbox, L1/R1 on the PlayStation) or, if you're playing with keyboard and mouse, alternate pressing the Left and Right Mouse Buttons. He'll pull out a shotgun and attempt to return fire, but if you keep shooting...
...you'll drive him back and he'll fall off the edge.