As someone who has completed arkham asylum and LOVED the combat system, I wanted to offer some tips.
1. The key to getting high combos is not getting hit, which in turn means mastering evasion (
) and understanding how it affects combos. Counters (
) look fancy and add 1 to your combo multiplier but they can be hard to time and pull off. If you dodge (
towards open ground) without touching an enemy you have roughly 1 second to land a scoring hit before your combo ends. However, if you evade (
over an enemy), your combo continues. You can Evade continuously and your combo will never break.
As a general rule, particularly when a round has a lot of enemies, it's better to Evade than counter.
2. Know your enemies. Knife-wielders can't be hit unless you stun (attack them by pressing
) them first or use a takedown on them. Stun baton wielders can't be hit except from behind (evade over them to get there) or with takedowns.
3. Use your takedowns judiciously. They're the easiest way to get weapon wielders down, so use your strikes on the base enemies and then use your takedowns on the knife and stun baton guys. Someone else will pick the weapon up eventually (you can delay this by staying in the area) but in the meantime you've bought yourself some free air.
4. Use your camera to keep your eyes peeled. If an enemy runs off, chances are he's going for a weapon, so use spare time (such as during takedown animations) to pan around and figure out where they are. On the maps with projectile weapons (barrels, bricks etc), keep an eye out for runners and either follow them or take them out with batarang (
5. Try not to use takedowns until your combo is 10+, otherwise you're taking out a guy you could 'milk' for more hits and thus more points. Once you get to combo values of 20 or more, you're generally best off to use takedowns as soon as they're available. Otherwise you risk eliminating enemies with strikes (10 points x combo value) rather than takedowns (50+ points x combo value).
6. Think really hard about how to end a round. Ground pound takedowns are the most valuable moves in the game. Ideally you want to finish every round with a quick batarang (to knock the last enemy down) and then ground pound him (100 points x combo). However, you need to carefully judge whether he has the health left to survive the batarang. If not, just use a normal takedown. Try to avoid finishing the last guy with counters or normal strikes. That last hit (assuming you've got a big combo multiplier) is extremely valuable and the difference between 10 points x combo and 100 points x combo can often add up to 1/3 or more of the round's overall points.
7. Favour defence over offence. Trying to land one more punch instead of evading will often be the difference between breaking a combo or not. Unless the clock is almost out, it's better to stay mobile and pick your battles.
8. To get silver medals (or indeed gold), its not always necessary to be completely untouched. You can often have a poor round in round 1 or round 2 and still earn enough points in rounds 3 and 4 to reach the target. Even in the later rounds, you can take a hit or lose your combo early in the round and recover to post a respectable score. However, if you lose your combo in the second half of round 3 or the second half of round 4, I'd advise you to cut your losses and restart the challenge.