Fortress Tower - Quick Time Event on the Bridge

When you regain control after the cut scene, keep Lara running forward, away from the man pursuing her. Because the camera is pointed at her while she runs into the foreground, you need to press Down instead of Up in order to keep moving.

An explosion blasts Lara and the man chasing her into the air.

As she grabs onto the end of the broken bridge, the burning man clings to her legs and tries to climb up her body to safety. In the next short quick time event, you need to wiggle the left stick back and forth or alternate tapping Left and Right on the keyboard to free one arm, grab your climbing axe, and elbow the icky dude in the head.

Then wait for the on-screen prompt and press the Melee button to finish him off.

If you're successful, Lara scrambles up onto the bridge.