A guide on how to find and complete the Shora Hah shrine and solve the "Blue Flame" puzzle.
How to Reach the Shrine
Go behind the Shae Mo'sah Shrine, and go northwest down a zig-zagging slope that goes down to the lava. Get into the mine cart at the bottom. Put a round Remote Bomb into the round compartment in the back of the mine cart, and detonate it. If the cart slows down too much, put another bomb into the rear compartment and detonate it. Be careful to move to the middle of the cart if you are near the edge, because you can fall out if you are too close to the edge.
At the end of the mine cart track, you will find the Shora Hah Shrine.
How to Solve the Shrine
Use Magnesis to lift up the spikes ahead of you. Carefully walk under the spikes, but avoid walking under the middle of the spike block, because Magnesis could deactivate if its tractor beam is pointing directly upward.
After you have gone past the spikes, you reach a crossroads. Go to the left to find some magnetic platforms leading to a blue flame. Before you go to the blue flame, move the magnetic platforms so you can reach the treasure chest. It contains a Royal Bow.
Then move the magnetic platforms so you can reach the blue flame. There is a torch beside the flame, so take it and light it with the blue flame. Then carry it back the way you came (make sure not to run or float, or you will extinguish the torch) and light the unlit torch with the blue flame. The bars will open.
Take out your bow and arrow and light it on the blue flame, then walk through the bars and go past the first two water spouts. Then shoot the blue flame at the unlit torch at the end. This turns off the water spouts and makes a platform start moving in the distance.
Go to the torch that you just lit, then shoot an arrow through it at the torch on the moving platform to the left. When you light it, some stairs rise from the lava.
Go back to the crossroads, and go up the stairs that appeared. Get ready to use Magnesis, then step on the switch and use Magnesis on the spiked ball that starts to roll toward you. Take the spiked ball up the ramp and up the stairs, then swing the ball from side to side to kill the Guardian Scouts in the area up above. Afterward, open the two chests in this area to get a Giant Ancient Core and a Great Flameblade.
Then go down to the moving platform and light your torch with the blue flame. Take the flame up to the area where you killed the Guardian Scouts, and light the unlit torch next to the bars. This will open the bars.
Go through and light the middle torch with the blue flame. If you try to light the other two torches, the water spout behind the torch will turn on, extinguishing the flame, so use Stasis on one of the water spouts, and light the torch next to the spout that you froze. Then light the third torch to open the bars.
Go through the bars and light the torch up ahead. Then get out your bow and arrow, and jump to light the arrow with the blue flame. Go to the middle, and shoot the two torches when they are lined up in the middle. The platforms will stop, and wind will start blowing upward between the platforms.
Float in the wind and land on the farthest of the two platforms and shoot an arrow to light the two unlit torches farther ahead. Then use the updraft to float to the torches that you lit.
Use Stasis on the water spout, then use Magnesis to push the blue torch past the spout before it starts pouring water again.
Then float in the updraft near the water spout that you froze. Look for a secret chest on the back of the nearby pillar. Float to it and open it to get a Forest Dweller's Sword. Then get in the updraft and float to the nearby ledge. Use Magnesis to pull the treasure chest to you. Open it to get a Silver Rupee.
Then use Magnesis to pull the metal platform all the way to the end where you are standing. Walk behind the torch and light an arrow, then shoot it at the leaves at the bottom of the ramp. This will kill or damage the Guardian Scouts at the bottom.
After you have dealt with the Guardian Scouts, open the chest at the end of the path to get ice arrows.
Go back to the blue flame and light your torch with it. Walk (don't run) to the next area, and light the nearest torch. Then stand on the square tile in the middle of the circle of torches and hold Y to charge up a spin attack. Let go to light all the torches. If it didn't work, make sure to center yourself on the square tile, and try facing the upper-right corner of the square before you hold the Y button to charge up the spin.
After you have done it correctly, the bars open. Go through and talk to Shora Hah to get the Spirit Orb.