Let's start on page 221, under Elements of a Monster. Under HP, it says HP is a measure of how much damage a monster can take before it dies, at which point it flatly dies. Just below that, it describes Special Qualities as "a guide to the fiction, and therefore the moves".
The crux of the issue with the Hydra is it has the Special Quality of "Only killed by a blow to the heart". As such, this overrides the more general rule about HP, and a hydra with 0 hp isn't, in fact, dead.
So, what happens?
You follow the fiction.
This hydra has taken enough stab wounds, magical assaults, and crushing blows to kill a dragon whelp, lich, or chimera. If a head was cut off and didn't regenerate yet, it's likely still gushing blood. It's still limping from that mace blow to the leg. That last magic missile to the heads probably just knocked it out, or it finally succumbed to the blood loss. Or maybe the Ranger got a lucky shot where the Wizard seared a hole in its chest earlier, and an arrow found its heart, killing it. But supposing it was only a flesh wound, the fiction should indicate the way it's out of the fight.
So, what happens next?
You follow the rules.
The Hydra lists "Regenerate a body part (especially a head)" as a Monster Move. Those are a specific kind of DM move. As such, that move is triggered at GM discretion (in lieu of any other DM move that could fit the fiction at the time), and when one of these three things happens:
- A golden opportunity (The rogue says "Do you guys think it's dead yet?", and it starts to quiver in response)
- A 6 or less on a player move (The ranger begins to search the body for the necessary healing potion reagents, and a new head forms and starts to sniff at him)
- Everyone looks to you to see what happens (nobody else is talking, and they're all looking at you like you're supposed to make a decision on something)
Or maybe none of those three things happen. Say the whole party decides they've vanquished the hydra, then wanders off. Pretty soon, the hydra will regenerate. If and when it does, the description requires that it come back stronger, and with more heads (if one was cut off in the battle). This is when the DM will follow the principles "make a move that follows", "think dangerous", "think offscreen, too", and "give every monster life". Those in turn help the DM fulfill the Agenda items "portray a fantastic world" and "fill the characters' lives with adventure".