[FussyZeus]

I believe Hercules solved this one by cutting all the heads off at the same time. So, in theory, you just need one guillotine per head.

[YeGoblynQueenne]

He cut the heads off and his nephew, Iolaos, cauterised the wounds so they wouldn't grow back.

So you'd also need fire.

Because "Of course you should fight fire with fire. You should fight everything with fire".