The Mirro Shaz Shrine is just outside of the Woodland Stable, which is where you'll be heading if you're completing the Korok Mask quest. Head in there so you can warp back to the stable easily in future.
The first challenge of the Mirro Shaz shrine involves hitting a ball over some distance to land it on an island in front of you. There's a chest when you walk in that contains an Iron Sledgehammer with extra durability, which will come in handy. Equip the sledgehammer and line yourself up so that you're pointing straight at the distant island. Use statis on the ball, and then hit it exactly five times. If you've lined yourself up straight, the ball will sail over and land in its pit, opening a path to the next area. If you miss, hit the switch to your right to summon another ball.
Next you'll encounter a block, which needs to be pushed up to lower down this sloped bridge. Again, you can use stasis and whack it five times... or you can just push the block, which is perhaps more fun because you need to walk up an extremely narrow beam. In any case, this bit's easy. Climb the ladder and walk up the bridge.
You've now reached the shrine monk and can wrap up if you want, but why would you when there's a whole other room? Follow the path to the left before you hit the monk and you'll find this elevator down into a whole other room.
For this one, you really need to make sure you hit the ball straight (look at all those obstructions!) but the tricky part of this puzzle is that the Iron Sledgehammer alone can't summon up the perfect balance of force. There's an extra Sledgehammer in the room, which should key you into its importance, but five hits is too many and six is too few.
So the key is to use statis, smack the ball with a sledgehammer five times, then quickly switch to a one-handed weapon, like a sword or boomerang, and hit it again. Think of it as needing to hit the ball 5.5 times.
It's tough to do (you'll have a much easier time if you've upgraded your stasis ability at the Hateno Ancient Tech Lab), but get it right and the ball will sail in.
Your reward? A Giant Ancient Core. These things are extremely rare: they can be used to buy weapons at the Akkala Ancient Tech Lab, or, more importantly, to upgrade some of the game's best pieces of armor at the Fairy Fountains. Head back to the monk to claim your Spirit Orb and you're done!
Need more hints? Check out the rest of our Legend of Zelda: Breath of the Wild game guides.