Perform well enough to unlock the Gold medal on all 24 Arkham City ranked maps as Batman. To unlock these maps, you will have to collect Riddler trophies during the main game. See "Genius" for more info on those.
There are twelve Combat challenges which are fairly easy. Focus more on keeping your flow going than throwing in a lot of variation. You're more likely to make a mistake trying to throw an explosive gel down than just using attacks, dodges and counters. When the titans show up, jump over them to confuse them for a few seconds. Against either of the twins, continually beat them and use Bat Swarm whenever possible to keep the other goons off you. You'll get your combo extremely high by the time they die and rack up the points.
The twelve Predator challenges are slightly more difficult. You'll have to perform three specific tasks in each map, all during the same attempt. Press at any time to view their requirements. Not too many tips I can give for these, the videos in the link below do better justice than words can.
Click here for a complete video guide to these challenges.
Note: Because he was playing on Easy difficulty, PowerPyx had the ability to recharge his smoke pellets. If you're playing on a harder difficulty, you'll need to slightly alter your play style compared to what he does in some situations.