The Stygian Dragon's "Chaos Fireball" changes damage type on each cast, so as others have mentioned, you want to try and max every resist. You will see the words of power above its head when it casts the spell, and if you are in a group you can anticipate the spell happening.
What you can't anticipate is it's area-like-earthquake attack. A person in all 70s will never die from a Chaos Fireball alone, but when hit with both the Fireball and the area attack, well, no one is going to survive that because it can do over 160 damage combined.
Best thing to do is use the teleporters, and as soon as you cast a spell or hit Stygian, pop out (and especially if you hear that Fireball sound, haha).
Since there is an Ankh in the peerless area, it's a rather easy fight for an accomplished group, but to solo it must be sort of insane. Unlike other monsters who tire and slow as their HP goes down, the Stygian remains quite fast, and its flight has a pretty cool AI, I must say.
The alternative is to use indirect spells, like summons, although, Stygian can do nearly 300 damage to an EV in one pop, haha. Rising Colossus can armor ignore though, so if you had a group of very good mystics you could try to kill the Stygian that way. It would take forever though.
Whatever you do, aim for cold damage when you attack.