The Breath of the Wild Hylian Shield is the most durable shield in the entire game. It’s hidden away in a dangerous area and guarded by a powerful boss, so you’re going to want to have plenty of arrows and a couple powerful spears with you on this quest.
The Lockup is behind Hyrule Castle, and the easiest way to get there is to paraglide over the moat from its northern side. The best location to do so is shown on the map below:
Once you’re there, paraglide over to the small platform straight ahead of Link in this shot:
Follow the pathway up slowly. There will be a stationary Guardian waiting for you. Run past and go into the doorway to its right to reach the entrance to the Lockup.
Once inside, you’ll be greeted by a closed gate with some water under it. Use the Cryonis rune under the gate to lift it up. Head inside to reach the Lockup.
Shoot the eye in the cell to your left to get rid of the Malice blocking your path. There are going to be all sorts of powerful enemies within the cells — ignore them and just run straight ahead until you reach an open doorway at the end of the hall. Go through and look to your right. You’ll see Stalnox resting as a pile of bones.
The only thing that separates this Stalnox fight from others is the enclosed space. Move as far away from Stalnox as you can and shoot an arrow at his large eye. He’ll fall to the ground, stunned, giving you time to stab away with a weapon. I find that spears work best because it gives you plenty of space between you and the Stalnox; if you get his by one of its legs, it’ll deal massive damage to Link. You can also get some hits off with a spear when Stalnox is standing upright, although it is dangerous.
Towards the end of the fight, Stalnox will cover his eye to shield against your arrows. There are a couple options here: aim perfectly to hit the part of its eye that is exposed, fire arrows into its torso to deal the remaining damage needed, or use a spear to stab at its torso.
When Stalnox hits near-zero health, its eye will pop out and bounce around the room. One hit to the eye will defeat Stalnox for good.
If you have Stasis upgraded to the second stage, you can freeze Stalnox momentarily, making it a little easier to shoot an arrow at its eye.
Once Stalnox has been defeated, a treasure chest containing the Hylian Shield will appear. The shied has a durability rating of 90 — the highest in the game. One thing to be aware of, though, is that the Hylian Shield can break. The only time I’ve seen this happen is after taking on several direct shots from the game’s final boss.