Sisyphean (adj.) comes to English through the Greek, and unlike last week’s word we know exactly where it comes from. It came into use in the mid 1600s (which honestly seems late) and is fairly rare in current use.
Sisyphus was, simply put, a cheating bastard. And he was good at it. Good enough to cheat death twice. After sufficiently pissing off the gods, either Hades or Thanatos (sources vary) was sent to drag Sisyphus to the underworld and bind him in a chair as eternal punishment. This was special treatment, as usually Hermes was sent to retrieve the souls of the dead. Hermes, psychopomp with elements of a trickster, would likely not have fallen for Sisyphus’ plan.
Sisyphus asked the god to show him how the chair worked. And, somehow not anticipating what was to come, the very embodiment of death and/or the underworld sat in the chair and was bound. This led to nothing being able to die, and the world becoming a rather unpleasant place. This was obviously an untenable situation, and eventually the gods conspired to make sure their brethren was released. Which once again meant Sisyphus was staring death in the face.
Before dying, Sisyphus gave instructions that his body should be desecrated after his death. And, on arriving to the underworld, he told Persephone such a sob story about how horribly his body had been treated. She was so moved that she let the smug little bastard go back to the world of the living to see to his affairs. Of course, Sisyphus had no intention of returning. Eventually, Hermes caught up with him and dragged him back down beneath the earth, but Sisyphus had enough time in the intervening period to be awful to his family and to basically make a nuisance of himself.
Once he was finally in the underworld for good, Sisyphus was tasked with rolling a boulder to the top of a hill. A hill which, upon reaching the top, the boulder would immediately roll down the other side. And this is where the word gets the meaning it carries today: something resembling fruitless toil towards an unreachable goal.