Nemesis are a game device that provide extra-damage for a hero and a villain. Some of them make sense, some dont.
The game mechanic sometime include Nemesis in the comic book sense, sometimes not. And Nemesis aren't always reciprocical.
Baron Blade <> Legacy Family : Blood feud that last for many generation, both are well accointed with the power/technics/capacity of the other and usually well prepared to fight each other.
Citizen Dawn <> Expatriette : Family feud, know well each other, Expatriette is supposedly an expert against Supers.
Grand Lord Voss <> Tempest : One slave with extra power rallying against his conqueror. Voss conquer Tempest planet so know the way to fight him, Tempest is extra dedicated to kill Voss and stop his invasion, and know his methods
Omnitron <> Omnitron X : self explatory, know thyself.
Plage Rat <> Chrono-Ranger : Chrono have a lot of experience now in fighting Plague Rats kind of creature. But little success against this one. Plague Rat is more intelligent that the common Chrono's prey, and probably escaped him several time already. He KNOW that the chrono-ranger is after him and thus prepare against him specifically.
Spite <> Wraith : Both Rook City citizens, know well each other, fight regularily one again the other. Is Spite the Wraith agressor ?
The Chairman <> M. FIxer : Known each other for a LOOOOOOONG time, the Operative is an ex-student of Mr. Fixer. Both are well fluent in fighting each other (and dedicated in eliminating each other).
The Matriarch <> Tachyon : Know each other, one hate the other. No justifiable reason Tachyon should be more efficient at damaging Matriarch, I would rather they she would be less efficient. Matriarch is fueled by hate. Possible explanation for Tachyon extra damage : being beaten by her unnerve the Matriarch and thus make her weaker, weaken her control of the birds.
Akasu'Bhuta <> Adepts Argent : cant justify why the hippy tree-hugger is the nemesis of a primordial chaos force... But thoses I dont know well, nor care about :p
Apostate <> Fanatic : Hate fueled rivalry, both know very well each other, know thyself.
Gloomweaver <> Nightmist : Occult detective and Voodo god, should come in competition very often so I suppose they both had trick ready against the other.
The Ennead <> Ra : Fight each other for millenium, self explanatory.
Haka <> Embuscade : Embuscade is there to kill Haka specifically so he is prepared. Haka isn't. But Embuscade is taking risk to get closer to him and his focusing on him, making him more easy to attack for Haka than other vilain.