Batman: Arkham Asylum

Every Predator Challenge gives you the chance of earning 3 medals by performing certain takedowns. At the start of each Predator Challenge, press Select (<) to view the required takedowns to earn the medals. The medals only gets saved if you complete the challenge by eliminating all hostiles.

As soon as you complete a challenge by eliminating all hostiles and have earned 8 or more medals, the achivement will unlock.

As soon as you have completed the required takedowns in achallenge, you are free to eliminite any remaining hostiles as you see fit. You are also free to perform the takedowns on any enemy, you dont have to make the first three takedowns according to the requirements. You may eliminate all but three hostiles and finish the challenge by using the required takedowns if you wish.

Sometimes enemies patrol in pairs. A good strategy to thin out the ranks is to stun them both and take out one of them and withdraw, letting the other one get up on his feet. It makes him an easier target for a required takedown.

The time does not seem to be a factor in the predator challenge other than placing you higher up in the leaderboards if you care for such things.

When starting the level be sure to press < at the begining to detail what takedowns are required for the level. The time doesnt appear to be an issue unless you're playing for the online leaderboards so just concentrate on the required takedown types. You have to complete the level (ie takedown all the guards on each level) for the awards to register.

Videos available upon this excellent guide from Batman5273: