You can find Zanmik Shrine in Hateno Village in East Necluda.
Shrine Location
Zanmik Shrine is located in Hateno Village in East Necluda, at 3469, -2179, 0148.
Scoop it Out
Up ahead, go down the ladder or glide down to the lower level. You will find a glowing device, and a large wheel over a pit of orbs. There are some squares of metal on the floor. Use Ultrahand to move a metal square onto the glowing circle on the floor, and move the metal square toward the other wire in the floor. This will light up the other wire, which makes the wheel start to turn.
Next, you can simply attach an orb to the spinning wheel, and it will become detached at the top when it hits the ramp. Or if you prefer to make a scoop, with one of the squares flat on the ground, attach two of the metal squares vertically, on opposite ends of the square, facing each other. Finally, attach the remaining metal square vertically so that it is touching the edges of all three squares. This structure will act as a scoop. Carefully attach it flat to the wheel so that it is only open on one side, and the open side is moving toward the pit of orbs.
Use Ultrahand to put an orb into the scoop, if the scoop doesn't catch any. The orb will be scooped up to the ramp above the wheel, and will activate the floor switch up above, opening the path to the end of the shrine. Note that your scoop will also become detached from the wheel, because it can't get past the ramp.
Before you go, you can also find a treasure chest beneath the orbs. It contains a Large Zonaite Sword.
Go up a ladder to the area above (or just use Ascend) and check on the glowing object to get a Light of Blessing.