I think it helped that my first (and second) runs of the game were each on hard. By the time that I got to the later challenges, I was almost disappointed that I could occasionally mess up and still get gold quite easily. Especially on the later challenges, I found myself restarting attempts that probably would get me gold out of frustration of some mistake I had made. Eventually, on one or two of the challenges, I got enough points to get gold with 2 mediocre rounds and one really good one. This wasn't even using the incredibly cheesy (IMO) tricks I saw on youtube.
Your first priority should always be to not get hit. Leap away from the action often, and don't let yourself get surrounded. Alongside this, if you aren't evading, you should always be attacking. Both of these points are probably incredibly obvious to anyone familiar with this game, but the basics are what they are for a reason. Beyond that, the best advice I can give is to find a routine that works for you utilizing as many of your tools as possible. If you can open a match removing several foes while utilizing as many different tools as you have access to (in order to build your combat multiplier), then you can relax the rest of the fight, relying on your instant takedowns to finish the job.
It has been a while since I did the challenges, but to the best of my memory, here's how I'd open a fight, assuming a large crowd. I'd first build my combo to 5 (just striking, and countering as necessary), and instant takedown the most problematic thug. I'd then leap to safety, triple batarang 3 thugs, claw a 4th, then ground takedown the furthest thug from me, assuring that the others can't reach me in time. From there, I just need to cape stun once, and I'll have maximized my combo multiplier. Assuming you don't break your combo, you'll have no problems reaching gold under these circumstances.
