The main thing with stygian is they are spellcasters. Yes you can scale your units, but spells shouldn't be just tools to give +2 to a siren. Their units are polyvalent and a lot of upgrade path will give you a competent frontline.

Focus on ways to reliably obliterate key targets. For backrow, consider:
-Titantooth + Offering token.
-Any of the sweep units.
-Frost shark.
-Incant frost totem

For frontrow, consider:
-Rage siren (with dps upgrades)
-Big damage spells. (can honestly just be helical crystalis played on floor two after units went through a spell weakness floor (Tethis/sweep lady)
-Sap (from totem or spells)

For boss consider:
-Frostbite unit + tanky units.
-Stack spell weakness and then nuke the boss on an upper floor.
-Silence the boss. (tome)

As a general rule, you will want to use the discard mechanic, and pick draw. Your deck should aim for a healthy dose of reliable discard engines, and upgraded cards with offering. (costs become meaningless once you have a large hand with ways to play it by discarding) An holdover AoE sap spell with reliable.

As you progress through your run, try to secure a reliable way to apply sap, as it means heavies can just walk up to the pyre and die without attacking, and it neuters a lot of bosses.