The Spiders Rune is located in the Slumbering Sanctuary. This is located in a random spawn in the area. I found this area to be extremely tough, the enemies are challenging. I would proceed with caution, especially when there is fog. There are fog spawners which hide enemies and I would advise to get rid of them immediately.
As long as you search through the area thoroughly you'll proceed to find the elite spawn. This elite spawn is none other than the Elite Caster. These are tough as they fire extremely powerful magic blasts. Try to avoid rolling 'backwards' as it will be a guaranteed hit on you.
To get to the Slumbering Sanctuary, this is the path you'll require to take:
Prisoners Quarters -> Toxic Sewers -> Ancient Sewers -> Insufferable Crypt -> Slumbering Sanctuary.
To get to these areas, you'll need the vine rune and ram rune. If you havent found them yet, I've linked my helpful playlist showing all the areas and runes on the game in order.