Nice, but potentially lethal (depending on how optimised your party is).
If I was to use this, I'd ditch the 5 acid damage if all attacks miss and the ongoing 5 acid on a hit, and replace that with an aura 2 acid damage 5 when bloodied. Simpler to track, but still nasty. Mainly I'd lose the triple fury attack when just one head is left: which at +10 damage per attack is pretty wild for a 6th level party.
This said, I'm not 100% sure why you've restricted the fury so it can't attack one creature more than three times? If the party's allowed it to grow seven heads, don't they deserve that pain, just like all the other hydras?
I love hydras, but in my experience, it's too easy for players in the know to prevent them regrowing heads - which is kind of their schtick - so I really like what you've done there (1 less head per 12 points of fire/cold). That's really neat.
Well, thanks for the feedback! In any case, one of the main concerns I had was that the party I have has very limited access to fire/cold damage--they had more, but apparently the shaman has decided to retrain out of scorching sands for something else.
As for comments on Acidic Fury, here's what I was thinking: I wanted it to deal damage even if it couldn't land an attack, but I didn't want it to be tied directly to Bite, as that would affect the power level of Snapping Jaws. So I figured tying it into Acidic Fury would work. I also thought that an aura and Snapping Jaws combined might be too much damage just for being there, so tying it to Acidic Fury meant the hydra at least still had to attack in order to deal the damage.
Of course, I wanted to word Acidic Fury in such a way that the 5 acid damage only affected a creature if it was A. missed by all of the attacks and B. only once per use of Acidic Fury. I didn't want to tie it into every single missed attack, as that would be too much. Along the same lines, making the extra benefit of ongoing 5 acid with the AC penalty a (save ends) effect makes sure it only affects a creature once per use.
The fight will likely be short yet brutal, as we do have a dual-wielding ranger in the party with a perfectly reasonable level of optimization (meaning he can dish out a ton of damage in one turn), along with 2 other strikers. This is a 6-person party, by the way. Bite by itself is rather low damage with only 3d6 damage, the only time a single bite deals significant damage is if it has 2 or less heads and it uses Acidic Fury (consider that this means it will only have 2 attacks with acidic fury). Also do consider that though 3d6+10 with three targets at one head can seem rough, it's about 20.5 average damage to 3 characters, which seems about right for a "critical" solo of the level (it can't possibly only have 1 head unless it's at a critical amount of HP). I figured I could get away with not giving the hydra any special powers when it's bloodied, as it naturally becomes more dangerous the more damage it takes.
Anyways, I'll consider everything and see if there's any adjustments I want to make. Thanks!