Zelda Tears of the Kingdom: How to clear the Lomei Labyrinths & Unlock the Evil Spirit Armor Set
One of the best aspects of The Legend of Zelda: Tears of the Kingdom is how the game makes use of its 3 main "layers" to the world; the surface, the sky, and the depths. Nowhere is this better utilized than with the game's 3 Labyrinths populating 3 of the 4 corners of the game's map - the South Lomei Labyrinth, the North Lomei Labyrinth, and the Lomei Labyrinth Island. These 3 locations task the player with trials across all 3 of the game's maps, and ultimately reward Link with quite possibly the coolest armor set in the entire game - the Evil Spirit Armor. So, how exactly do these work?
Clearing the Lomei Labyrinths and Earning the Evil Spirit Armor Set
While there are 3 Labyrinths across the game world, all of them share a very similar structure; start on the surface, and find the path forward to the end of the maze to not only unlock a Zonai Shrine with a free Blessing of Light, but also to unlock the ability to challenge the upper portion of the same Labyrinth floating in the Sky Islands above; once you activate every terminal in the above Labyrinth, you'll unlock the grate in the Labyrinth on the surface - allowing you to dive straight from the Sky, into the Depths, and then challenge a Flux Construct III to earn a piece of the Evil Spirit Armor.
Every one of the Lomei Labyrinths follow this framework; the layout might be different once you're inside, but they won't deviate from this structure. Furthermore, there's a very easy way to find your way to the end of the Labyrinths on the surface - a researcher, presumably Calip from Kakariko Village, has already charted the course to the end of each of the mazes with a trail of nuts or acorns leading the way to the end. If you follow this trail you won't have any trouble keeping your bearings.
As for the Sky portions of the Labyrinth; you'll actually have the locations of the terminals you need to activate on the Adventure Log, and you'll also be able to see their rough locations on the map, assuming you've already activated the Skyview Tower for the area in question. While it might be a little more difficult compared to the Surface, it still shouldn't pose any significant issues. By far the most difficult portion of tackling any of these Labyrinths will be the portion in the depths, where you'll have to face off against one of the more challenging boss enemies in the game - a Flux Construct III.
After you've defeated your enemy, and activated the terminal, you'll gain access to a chest containing one of the pieces of the Evil Spirit Armor set. The Evil Spirit Mask can be found in South Lomei Labyrinth, the Evil Spirit Greaves are obtained at North Lomei Labyrinth, and the Evil Spirit Armor chest piece is waiting for you at Lomei Labyrinth Island.
Where to find, and reach, the Lomei Labyrinths
The North and South Lomei Labyrinths can be found slightly off from the Cardinal directions of Hyrule, while Lomei Labyrinth Island is found at the Northeast Intercardinal direction of Hyrule. South Lomei Labyrinth is found in the Eastern portion of the Gerudo Desert; right on the border between the Gerudo and Faron regions. North Lomei Labyrinth is found in the Northeast portion of the Hebra region, in the far reaches of the Tabantha Tundra. Lomei Labyrinth Island is off the coast of the main continent, to the Northeast of the Akkala region.
Reaching the Labyrinths on the Surface isn't too tough of an ask, though considering the North and South Labyrinths are in areas with extreme environmental conditions, it's advised that you take caution while exploring them. As for the Lomei Labyrinth Island, you will need to either glide over from the cliffs at Akkala, or make use of a falling fragment of a Sky Island. Getting to the Labyrinths in the Sky is a bit trickier, though if you have Autobuild unlocked and some spare Zonaite, you could always launch yourself from a tower to the nearest Sky Island, and then make use of a makeshift plane to ferry you to your destination.
Naturally, getting to the portions of the Labyrinths in the Depths is easy; once you've finished the first two sections, you can simply dive straight into the chasm connected to the lower portion of the Labyrinths from their respective branch in the Sky. Best of luck with your journey through each Labyrinth, and have fun!