Get to Higher Ground

Lara is in the water struggling. The current takes her along. At the first obstacle steer left or right to avoid collision and ultimately death. After that keep in the middle till the next obstacle appears in the path. Again pick either left or right to evade, although left is a little easier overall as it gives you more time to react when the paths meet again. When you've taken the left path, and have evaded the little obstacles on the way, you need to evade the bigger obstacle by steering to the right.

Diving

Lara hits a beam that is blocking the path but she is unable to hold on to it. She however manages to grab the wooden door of a hut on the right which bursts open. Struggle against the current to grab the other wing of the door. The building opposite collapses and Lara is pushed under water. Dive through the doorway into the light filled room. Behind the first obstacle is a pocket of trapped air where Lara can catch her breath. Continue towards the red exit sign. The door there is locked but can be pried open using the axe. In the next room ascend towards the headlights of the ruined vehicle. Enter through the hole in the windscreen and move through the van to the back. Use the axe to break the back window by repeatedly pressing the melee attack button (PC: F, PS4: Triangle, Xbox: Y).

With the Current Again

Lara surfaces again and she manages to hold on to a sturdy pole for a moment, before the journey downstream continues. Steer to the right to avoid the next obstacle.

Running, Jumping

Lara manages to reach a roof. Pull onto it. But it's not safe for long. Run ahead and jump to the light-grey ramp. From here jump towards the billboard floating past and perform a saving grab, so you don't slip into the current. Pull up and balance to the left end. From there jump towards the dredger. Balance up its arm and jump towards the horizontal bar at the lamp post to swing to a roof. Lara slides down onto the remains of a walkway. Run along and jump to the next lamp post to land on a container sailing by. Jump towards the remains of the next walkway, which will collapse underneath Lara. Run along and towards the wall of the taller house.

Climbing

Jump to the craggy wall and use the axe to grab it. This is where the achievement/trophy Recipe for Disaster should pop. Climb around the corner to the left. Jump towards the left to reach the red boards and when touching them with the feet immediately jump again to perform a double jump and reach the upper ledge. Pull up. Face the wall of the building and perform a double jump to grab the window sills above. Traverse to the right and jump across the gap to the next sill. Shimmy around the corner and climb along the sills, jumping the gaps. After witnessing the gruesome death of a child, and reaching the burning window, perform a double jump and climb up the ledges to the top.