This whole section is a series of action sequences, which start by grabbing onto a rope. When you regain control, wiggle the analog stick down (or press the direction key) to start running from enemies.
One of them will grab Lara, forcing you to perform a QTE sequence. Wiggle the analog stick left and right (or press directional keys), but be ready to tap an indicated button when it shows up (screenshot).
The next sequence is less complicated. Run and jump as the bridge collapses under your feet (reward: 100 XP).