Spider King is a miniboss located in Holodeck 1, the most basic level. You can find him in the deepest parts of the nest, and it's easy as he's the largest spider there.
The Spider King will continually send his minions towards you, eroding down your armor and being a general pain. Be sure to hit him in the times he's brave enough to face you himself. His other attack makes it even harder to approach him by covering you in webs.
Afterwards, you can find a chest by the portal containing a few Steel Ingots. Make sure you hold on to those.