The Orochium Shrine of The Legend of Zelda: Tears of the Kingdom is one of the legitimately challenging puzzles that punishes those who try to unfairly gimp its puzzle. For this puzzle, the long and slow approach is typically the way to go – no easy way out.
Located in the bitter tundra of the Tabantha Snowfields, it is one of those shrines you'll need to face if you want a teleportation spot in a location as crucial as Orochium's (beside the Snowfield Stable). However, it'll certainly be worth your while in convenience and the extra blessing.
How To Complete The Orochium Shrine: Courage To Fall
From the beginning, you'll notice two large doors you can grab and open with Ultrahand. You can't do anything with these for now, so ignore them and take the path to the left.
There's an enemy Zonai over here with a Long Stick, so defeat it quickly and beware of its range in the process.
Ahead, use Ascend to rise onto the platform above where you'll spy a ladder. Climb it and turn right to crouch through a small tunnel.
Turn right again and look down to spy a second Zonai below.
As you drop from here, draw your bow and fire a few shots from above before you land. If the Zonai is still alive when you do, finish it quickly.
Go around the corner and ignore the stairs, for now, to fight the Zonai guarding a chest with five arrows. Grab these arrows and return to the stairs.
At the top of the stairs, use your Ultrahand to open the doors. On the other side, your path will be blocked by several lasers that will trigger a pit trap if you touch them. However, that's exactly what you want.
Step into the lasers and drop into a long hallway chamber filled with even more lasers. You don't want to touch these.
Run around all of these lasers and beware of those moving. You'll want to take the utmost caution here, as being struck with these will cause you to restart the puzzle.
Once you reach the end, use Ascend to rise into a chamber with a chest containing a key.
Use Ascend again to leave this chamber and return to the main level. Turn around to face both of the Zonai ahead on either side of the room containing an orange, small ball.
With the Zonai dealt with, you can now circle around the central chamber to the locked door. Use your key to enter and take the orange ball inside.
Carry the orange ball back to the stairs behind its room (the set you descended to fight Zonai after Ascending from the chest's chamber).
Use one of the rising and lowering platforms on either side of this upper section. It doesn't matter which you choose.
At the top, place the ball in the circular switch to open the gate to the left. Inside is a glider you can take out with Ultrahand.
Place the glider outside the gated room and then attach the ball to the top of it. With the ball secure, you can now place the glider on the rails ahead before jumping on.
From here, step onto the front of the glider and carefully maneuver it down toward the end of the shrine, where the next glowing sigil for the ball can be found.
Once you land, you can detach the ball and place it in its rightful place. This will open the door for you to finally claim your prize and leave.