Removing and cauterizing the fire-resistant head strips the hydra's body defense and allows persistent flame to damage the whole creature.
Every hydra head supplies a resistance and corresponding attack. The central body ignores Carl's direct bomb and remains hard to damage magically.
Randomly destroying a head only suspends its resistance while the neck regenerates. Permanent progress requires a flat decapitation surface, identification of the fire-resistant head, and immediate cauterization.
Carl narrows the candidates through observed attacks and failed fire damage. He identifies Bea's mother, uses a snap collar and shrink wand for a clean cut, and smashes moonshine against the stump.
A health bar finally appears and the fire on the hydra's back begins damaging every remaining head. Shi Maria can then remove heads without needing each resistance solved independently.
A hydra neck sealed by flame after a clean circular cut, causing the whole stitched body to ignite.
The vulnerability is the central puzzle that converts an otherwise nearly invulnerable city boss into a killable target.