a Herculean task

Hercules was the strongest man who ever lived, a son of Zeus born with a strength no mortal could match. It bought him no peace. The goddess Hera hated him, and she sent a madness upon him so terrible that in its grip he destroyed his own family. When the madness lifted and he saw what he had done, grief broke him, and he went looking for some way to atone.

The oracle gave him his penance. He was to enter the service of a cowardly king and perform whatever labours the king set him, and the king, prompted by the spiteful Hera, chose the most impossible tasks the world could offer.

So Hercules set out to do things no other man could dream of. He strangled a lion whose hide no weapon could pierce. He cleaned in a single day the filthy stables of a thousand cattle, thirty years unswept, by bending two rivers to run through them. He hauled the three-headed guard-dog of the underworld up into the daylight with his bare hands.

Each labour would have been the end of an ordinary man, and there was not one or two of them but a whole series, each seemingly harder than the last. Yet by sheer strength, endurance, and a refusal to quit, he finished every one and won back his honour.

A Herculean task is a labour on that scale: a job so vast and so punishing that it demands almost superhuman effort, and only the strongest will can see it through.