Not sure if we are talking about the same thing....The "Combat Challenges" are in a different section from the main story. (one block to the right, I think, if you are choosing from the menu, when you start the game.)
In it, there are a series of combat, and stealth mode "challenge maps"...unlocked from different points in the story, and through actions and Riddler Trophies...)
The Fighting challenges are 4 rounds of a set amount of enemies, each round...getting progressively more numerous, and difficult...you get additional points for stringing combos, not getting hit, gadget bonus', etc...
The Stealth challenges are a series of captures and knockouts, utilizing all your detective skills, while not getting detected.
Sorry, if you have already discovered these, disregard,...but they do go toward your completion.