Nemesis is a stronger word than enemy.
Enemy is an unfriendly or hostile person. Nemesis is an avenging force.
In classical mythology Nemesis was the goddess of retribution. She punished both hubris (false pride) and wrongdoing. The goddess represents the idea that one cannot escape divine retribution.
Lowercase nemesis came into the language in 1597 with the meaning “retributive justice.”
One of my favorite Agatha Christie mysteries has the title Nemesis. In it Miss Marple is portrayed as Nemesis, tracking down a murderer many years after the crime was committed.
Conan Doyle called Professor Moriarty “the nemesis of Sherlock Holmes.” If it hadn’t been for the insistence of outraged readers, “The Final Problem” would have been the final Holmes story. It ends with Holmes and Moriarty plunging to their (presumed) deaths from the top of the Reichenbach Falls. Each was the other’s nemesis.