This has to be one of the vaguest questions I've seen in a long while.
First off, the combat system in a Batman game is actually a wide array of game mechanics, each with their own pacing and distinct feel.
Don't let the fact that the game makes it easy for you to learn this system fool you into believing this is by any stretch 'simple'.
You probably wouldn't believe the amount of time that countless individuals have spent to get the right timing, that extra tidbit of feedback, that additional tool/combat move/combo just to make sure that, in general, the combat would feel great... and up to the very last minute, despite having almost everything, it must've been fairly dull.
To be specific, how do you actually go about adding mechanics like that in your game? How do you make your own fighting system like that?
It takes many visionaries. From my limited experience in this specific type of system, I'd say that, at the very least, you'd need someone with clear creative control (game director or game designer), someone with a more down-to-earth approach (game designer) and someone to actually prototype the actual idea (gameplay programmer).
Then, you need someone with clear modeling skills, a rigger, and an animator just to get your core character and a dummy enemy into place. You can probably start trying stuff from then on.
Before the end, you'll need someone to texture, quite possibly an FX artist of some sort (for all of the nifty special effects you see in combat), and a bunch of other folks I'm probably forgetting about (oh, and a sound designer, of course!)
On a title I've worked, they've sent the 'combat' team to train in martial arts for a few classes before even delving deeper into the actual development.
Their team was of about 10 people, 3 of which were specialist programmers (fully dedicated to the combat only), 1 was an animator, 1 was a sound effect designer, and I can't quite remember who the others were as I was not immediately tied to that subgroup.
If your intent is to prototype a full combat system on your own, you're looking at a lot of work. Try starting with a clear and concise idea of what you want it to feel like, then model/rig two characters (possibly one and its clone) to serve your purpose.
Then, prepare the actual animations you'll use for this, and finally delve into the actual coding/integration.
If your overall plan makes sense, you could end up with something that works.
If it looks good, do the final touches (add the textures, fx and sfx).