Part I: Humans would migrate and settle
Humans are remarkably adaptable to radically different environments; most other large animals aren't. We would instinctively or even incidentally take advantage of that.
Ravenous tropical/subtropical predator that relentlessly hunts humans? Nomadic populations would migrate towards the poles, settling in freezing arctic climates. Dressing themselves in thick hides and furs, and hunting lesser arctic wildlife, humans would soon adapt to an arctic way of life, while the bone-chilling cold would deter any significant incursion.
Polar bears on steroids? The reverse would happen; humans would move into dense tropical jungles and arid desert areas where the creature's fur and fat that enable its survival in arctic regions would rapidly exhaust and kill it. Humans would wear minimal clothing and develop lightweight and portable shelters; in arid climates water would become a commodity.
Vicious jungle beasts? As with the bears, humans would find arid climates to their liking. Storage of water and development of temporary/portable shelters would allow them to adapt, while the unavailability of water would swiftly dehydrate the (likely high metabolism) predator. The only advantage it might have here is if it discovers that humans have water skins, and swiftly tracks from settlement to settlement, tearing into their water supplies after attacking to rehydrate.
Part II: Humans would kill the predator
Once humans settled in a climate hostile to the predator, they would have time to start developing more advanced tools (including activities such as mining and smelting, to start producing metals)... and sooner or later their collective interests would turn towards killing the predator.
I would be entirely unsurprised if unrelated settlements (which would naturally evolve into villages and then cities over the course of generations) start getting the same idea in different geographic locations, and then begin fighting back, squeezing the predator population from multiple sides until it eventually collapses.
Thanks to communications skills, storytelling, and eventually the written word, humans would definitely hold a grudge against this one animal they cannot dominate or domesticate, and as technological advancements bought them more free time they would devote that time to conquering the beast. Between the human ability for strategization and group tactics, and development of specialized hunting tools and traps, sooner or later it would find itself on the losing end of the dominance order.
Part IIIa: The predator would go extinct
Due to the long and antagonistic relationship between humans and this super-predator, once humans developed the technology and strategy to fight back, they would likely make concentrated pushes against it, focusing on destroying nests/killing young. Initially it'd just be to reduce the thread posed, but once we securely have the upper hand there's no reason to leave it to chance, and we'd continue pushing until it posed no threat any more. At best, if we've evolved socially and technologically far enough by this point, we might keep a few specimens captive in zoos, and the beast would live on in stories told to keep little children in line.
Part IIIb: Humans would domesticate it
Humans like to put animals to use. Whether raising them for food, transportation, or other utility -- even sport, humans have a long and rather successful history of domesticating animals. As soon as they finished with Part I, they would probably start domesticating lesser animals, and eventually some industrious humans would get the bright idea to start domesticating the super-predator.
Some cultures might domesticate it for sport, pitting them against one another. Others would domesticate it for defense or war, unleashing them on the enemy to cause major casualties or at least serious distractions. Still others might train it as a hunting animal -- if it were successful enough at hunting resourceful humans, it no doubt has attributes well suited for hunting. Repurposing these hunting and tracking skills to exterminate lesser threats (wolves, coyotes, and others that interfere with domestic livestock), counter greater threats (any wild super-predators still surviving), or hunting wild prey (tracking and perhaps chasing big game) could prove very useful to advancing human civilizations.