In the DCU, Batman isn't the best fighter (last I recall) but rather the benchmark to which others are rated. Lady Shiva is the best fighter if I remember correctly (at least way up there and better than Batman).
I was wondering who's the best in the CU? Best villain one? Best hero one? I'm actually looking for the best villain one specifically, but would like to just get a run down of the best hand to hand fighters in CU.
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The Tournament of the Dragon is to some extent analogous to the Mortal Combat of the games/movies/series of the same name. A great martial-arts tournament is held every sixty years to choose the world's mightiest martial artist, to face the full manifestation of the evil entity called the Death Dragon. Victory for the champion means the Death Dragon remains trapped in another dimension for six more decades. Defeat means the Dragon is free to wreak chaos across the Earth until the end of that sixty-year cycle. For specific metaphysical reasons the Dragon is most effectively confronted by a single martial-artist opponent.
Joybuzzerx, I'm guessing from the character examples you mentioned that you're interested in hand-to-hand fighters who are essentially physically human, or comparable to human, rather than superhumanly strong or fast, or who also have ranged powers. There are a number of highly skilled HTH combatants in the CU who exceed the limits of a normal human body, or use technological or magical artifacts to enhance their physical prowess.
There are also people referred to, but given no game stats, who might exceed the skills of any of the characters actually statted for the PnP game. Their concepts could accommodate that possibility, but there's no way to compare them to be certain. In any case their location makes it unlikely most PCs will ever randomly encounter any of them.
So, confining ourselves to "human" fighters as described above, perhaps the most formidable combatants today are the mercenary villain and would-be crime lord called Jade Phoenix, and his hated rival, the superhero known as Nightwind. Both men studied at the legendary (but now destroyed) Yengtao Temple, where they learned the most advanced martial arts techniques, and are now among the very few masters of them left in the world.
Other very skilled HTH combatants include the mercenary villain Green Dragon, well-versed in many substyles of kung fu; the hero Redsnake of Vibora Bay, greatest living master of the art of Vibora Carmesi; and Spirit Fist, once a member of China's national hero team, the Tiger Squad, who could no longer support China's Communist government and now works from abroad to overthrow them.
There are certainly other fighters who could match and perhaps exceed any of the above, but most of these possess true superpowers or use special weapons.
Jade Phoenix and Green Dragon, in particular, are arrogant, very sensitive to insults, and jealous of their skills. Either would gladly kill anyone who insults them, or just has fighting skills even close to rivaling their own.