PixlBit

I can get the stealth stuff pretty well as far as challenges like take a thug down x way, etc., but while the fighting challenges seem more obvious, I'm having a real hard time figuring out the best way to get the high scores. I have to really try and get the variation and Dark Knight bonus on each stage of the fighting levels to even crack the 6,000 points mark. Any tips? 

Also, is $19.99 for Arkham City on Steam worth it, or should I wait?

i didn't really focus on this stuff when I played this...  i think combos are the key, and not getting hit when you're fighting, and generally not taking much damage.  Arkham City is a great game too, just different and more open world. But it's just as good. People argue over the two all the time. 

The new one, Arkham Origins, isn't great, but is still okay.  City is great, but you could always wait for a sale too, it's often on sale at various sites like amazon, etc. 

I'm about half way through Asylum on a second playthrough and think i'm pretty decent at the game. That being said, I suck at the challenges. I think as Matt said it's all about avoiding getting hit and variety but it's tough. As for Arkham City, it's a really good game (50/50 on which is better Asylum/City) so if you want further story material go for it. Thing about steam though is there's always a sale around the corner

I figured about the not getting hit (Dark Knight bonus) and variety bonus, but even when I do that I wind up w low scores, so must need more variety.