Allegedly she was so hideous that anyone who gazed upon her would be petrified. It was her contrarian personal aesthetics that killed. Lethal vanity.
It's very Lovecraftian. Maybe its a Color Out of Space sort of thing.
Basillisks sometimes had to lock eyes to petrify, though the cockatrice version spit extremely corrosive acid. I suspect there's a link by storytellers unifying their world building.
I know of some women who have practiced a withering stare that can paralyze with fear or shame. I seek to master such techniques.