A guide on how to find and complete the Kam Urog shrine and solve the "Trial of Passage" puzzle.
How to Find the Shrine
This shrine is in the Hateno Region. Go to Ha Dahamar Shrine, and go east on the road in this area. You will reach Fort Hateno. Look for the cabin in the forest. You will find Doctor Calip in or near the cabin. Talk to him to get a shrine quest, with a hint for finding the shrine.
Check on a fire and sit until night. Then go east along the road that goes through Fort Hateno. Look for a path going northwest. Go to the end of that path and you will find many statues. At night, one of the statues will have glowing eyes. Shoot it with an arrow to make this shrine appear.
How to Solve the Shrine
Go straight ahead and enter the rotating area, but watch out for rolling spiked spheres. You can use Magnesis to remove them. Stand on the left side of the rotating area such that the rotating platform will be under you. When you can, float to the treasure chest in the opening in the wall. It contains an opal.
Then turn around and wait for the platforms to rotate such that you can float onto the rotating platform that has a treasure chest on it. Open it to get a Soldier's Spear.
Get on one of the longer rotating platforms, and when it's horizontal, use Stasis to stop the wall gear, then jump from your platform to the spinning gear in the middle, then jump across to the other long platform, and from there jump onto the platform with the glowing light on it. When the wall gear starts spinning again, wait for your Stasis rune to recharge, then ride up the gear until you're near the top, and use Stasis to stop it again. Then jump onto the platform at the top and go up the short flight of stairs. Turn around and look at the wall gear, and when you see that a long platform is horizontal, use Stasis on the wall gear. This should stop one of the stairs such that you can go up the stairs to the archway at the top.
From there, you can go up and talk to Kam Urog to get the Spirit Orb.