This page explains how to find the Shai Utoh shrine and solve the "Halt the Tilt" puzzle.
How to Reach the Shrine
Go east on the road that goes past Pumaag Nitae Shrine. After a while, you will pass the Lakeside Stable. Look in the cliff wall behind the stable for cracked stones. Bomb them to find a cave that contains this shrine.
How to Solve the Shrine
Use Stasis on the see-saw so you can walk up it without making it tilt down. Do the same with the next see-saw that you find. If you go up this see-saw in the direction that it started in, you will reach a treasure chest that contains a Traveler's Sword.
The treasure chest is metal, so when you're done, use Magnesis to move it to the next area of the shrine.
Then step on the high end of the see-saw to make it tilt the other way, then use Stasis to freeze it so you can walk up to the other side.
With the next see-saw that you find, stand on the end closest to the flat see-saw up above, then use Magnesis to drop the metal treasure chest on the other end. You will be launched to the second treasure chest, which contains an Ancient Core.
After you open that chest, you can use Stasis on the flat see-saw and glide down to it to reach Shai Utoh.