This page explains how to find the Mogg Latan shrine and solve the "Synced Swing" puzzle.
How to Find the Shrine
Go to Rota Ooh Shrine and go north on the road. Continue along the road until you reach Manhala Bridge. Cross the bridge, then go northwest when there is a fork in the road. Go north across Nima Plain to the grassy slope leading up to the mountain. Make your way to the top of the mountain and you will find the shrine just south of the three peaks.
How to Solve the Shrine
Jump onto the swinging metal platform (use Magnesis to make it swing more if it has slowed down) then jump off at the other side. Use Magnesis on the next swing to pull it toward you and then jump onto it and jump off at the other side.
On the other side, there is a bridge being held up by ropes. Shoot the ropes. You might need to throw a bomb at the bridge and detonate it against the bridge to make it fall down.
Cross the bridge and open the treasure chest to get a Forest Dweller's Spear.
Then use Magnesis to push the spiked balls out of the way. there is a treasure chest after the last spiked ball. The chest contains a Forest Dweller's Bow.
Then go back to the stairs before the last spiked ball, and pull the magnetic block toward you. Then turn off Magnesis and step onto the block. It will slide down toward the other blocks. pull the lowest one closest to you and step on it, then pull the second lowest to you so you can step on it, then do the same with the third. From here, you can glide down to the treasure chest, which contains a gold rupee.
After you open the chest, pull the blocks so you can go up to the third one. Then you can pull the fourth one toward you and go up above. Hit the crystal switch to make two fire lanterns fall from above. The lanterns are magnetic, so you can make them swing. Swing them, then shoot the lantern's chain when the lantern is above the dry leaves. Or if you have fire arrows or a fire weapon you can just burn the leaves that way. Then push the magnetic doors open with Magnesis. Talk to Mogg Latan to get the Spirit Orb.