Move forward and use the climbing axe to unlock the door. Enter the Solarii Fortress. There's a very linear trek ahead of you, though made more interesting by numerous explosions and interactive cut-scenes on the way.
Take the right corridor. Approach the collapsed area and wait for Lara to automatically crouch and get you through. Don't attack any guards, they'll be much more occupied with escaping the fortress. You can search their bodies, though, if they're not too close to the fire.
Turn right again, into a burning corridor, and locate a hole in the wall. Follow the linear path and leap up to a roof fragment. When you do, turn left and jump again. This time you'll have to use the climbing axe.
At the top of the interactive wall, lean out to the left and leap over to the adjacent platform occupied by a burning enemy. Continue forward. When you enter one of the next rooms ahead, the game will trigger cut-scene.
As soon as you regain control, follow your enemies' footsteps to get to a zip-line, and slide down it. Take cover when you land; there are some enemies to the right. First, take care of the dynamite-throwers, especially since you don't have much room to move and the wall can be gone very quickly. Get rid of everyone.
Drop down to the roof fragment below and stand as indicated. Leap over to the edge of the adjacent building. Lara will probably lose her grip, so tap the action button.
Scramble up to the rooftop, approach the interactive wall and use the climbing axe the usual way. Examine the bodies, then take the only available corridor, which leads north-east. The game will trigger more cut-scenes soon - Lara will retrieve all her lost gear and proceed to the main battle of this section (reward: 100 XP).