This page explains how to find the Mirro Shaz shrine and solve the "Tempered Power" puzzle.
How to Find the Shrine
The Mirro Shaz Shrine is near the Woodland Stable, which is just south of Woodland Tower.
How to Solve The Mirro Shaz Shrine
Follow the path from where you entered the shrine. You will reach a ledge that you can either jump off of and float down, or you can wait for the floating platform to come up.
At the bottom, open the chest to get an Iron Sledgehammer.
Then use Stasis on the puzzle orb in the middle of the raised platform, and hit it with the Iron Sledgehammer (or another heavy weapon) five times. If you aim it correctly to land in the hole under the Sheikah Symbol on the arch in the distance, the orb will roll into the target. This will make the nearby wall rise. If you need a new orb, hit the crystal to make a new one appear.
Go to the new area, then use Stasis on the cube that is attached to a rail. Hit it with the Iron Sledgehammer six times and it will make the see-saw fall. Climb up a ladder, then go partway up the see-saw, then use Stasis on it so it won't fall when you walk onto the upper half. Go past the see-saw and you will see Mirro Shaz in the distance.
However, if you want all of the treasure chests in this shrine, before you talk to Mirro Shaz, go into the caged path next to his platform, and you will find a new golfing area. The chest here has another Iron Sledgehammer. Use Stasis on the orb, but this time, hit it five times with the Iron Sledgehammer (or another heavy weapon), then hit it once with a sword or other light weapon. You will have to do it quickly before Stasis runs out, unless you have upgraded your Stasis rune.
Once you make the orb fall into the target, the nearby gate opens, and you can open the chest inside to get a Giant Ancient Core.
Then you can go back and talk to Mirro Shaz to get the Spirit Orb.