In Hades, you play as Zagreus, son to the god of the underworld. He wields six different Infernal Arms to break out of hell and reach the surface world.
Each Infernal Arm has 4 Aspects, or variant forms. The Stygian Blade's final form is the Aspect of Arthur which transforms it into Holy Excalibur.
Not only does Holy Excalibur add 50 to your Life total, but its Special Nova Smash leaves a Hallowed Ground aura that reduces damage, disables traps, and slows enemies and their projectiles.
So how do you get it?
Step 1: Unlock the Aspect of Guan Yu for Varatha, Eternal Spear
To do that, follow these steps:
Purchase the Fated List of Minor Prophecies from the House Contractor
Reach the final boss
Invest 5 Titan Blood into non-Zagreus weapon Aspects
Talk to Achilles
You'll probably unlock the Aspect of Guan Yu by progressing naturally through the game. Talk to NPCs every possible time, buy the Fated List of Minor Prophecies ASAP, and invest in weapon Aspects other than the default forms.
Invest 5 or more Titan Blood into Blade Aspects
Spending 5 Titan Blood on the Stygian Blade should be easy. The Aspects of Nemesis and Poseidon are best here, as they overlap with the Aspect of Guan Yu unlock conditions.
Talk to Nyx to receive the special unlock phrase
Once the other requirements are met, there's a chance that Nyx will give you the phrase that unlocks the sword...
"I see your kingly pardon from a prison of stone."
Interact with the Stygian Blade in the courtyard and spend 3 Titan Blood to unlock the Aspect