To complete the trial of the serpent in the hidden city in the head of the serpent in Shadow of the Tomb Raider use a rope arrow to pull the lever on the wall. Then use the serpent head to burn the blockage. Go down to the two pillars and use a rope arrow to attach the pillar without a handle to the pillar with the handle. Go over to the pillar with the handle and turn it so that the pillar without a handle is turned to allow the liquid to flow to the barrier.
To get past the flammable barrier in where the twins confer in Shadow of the Tomb Raider craft a fire arrow. On PS4 the button is R1. Then aim the bow at the barrier and press R1 to shoot a fire arrow.