To complete the Path of the Battle challenge tomb in the Hidden City in Shadow of the Tomb Raider go to the middle area and walk over to the left exit ahead whilst jumping over any totem arms that swing your way. Drop down and follow the path to the lever ahead. Pull the lever back and quickly make your way around the right side of the area avoiding any traps by jumping and ducking as required. Pull the lever to lower the totem pole by one layer.
All The Hidden City Guides
All Shadow of the Tomb Raider Guides
Go back around the middle area jumping over the lower totem arm and ducking under the raised totem arm. Use the far exit and jump down. Go to the lever the raises the arms of the totem pole and pull it back. Quickly make your way around the left side again dodging and jumping over any spikes. Pull the lever to lower the totem pole once more. Climb the totem pole to the top to complete the path of the battle challenge tomb.