I am throwing this up as a placeholder until someone posts a proper solution. The point of this guide is to warn people that one of the challenge maps requires the
Sonic Shock Batarang rewarded for
Worst Nightmare rank 10. If you have any interest in completing the challenge modes this time, you need to be ever mindful of this and begin working on it immediately in your first playthrough. Please see the guide for Worst Nightmare to give yourself an idea of why.
Overall, this is quite a bit easier than any character's campaigns in Arkham City. For those new to this play mode, a campaign is a series of three challenge maps that need to be completed in one sitting. They can be all combat, all predator, or (most often) a mixture of both. You have three retries to use on the latter two maps; retries on the first map do not count against you. In addition, you have six mods that must all be used over the course of the campaign, you decide which mods to apply to which map. Otherwise the medal requirements are exactly the same as the Ranked Challenge versions of the maps. For the achievement, you must get all nine medals in every (non-DLC) campaign, or eight and the free medal mod if available. The DLC campaigns are on a separate page from the rest and are neither required or counted towards the achievement.
As far as the mods, you generally want to take Time Limit, Gadget Malfunction, Decreased Health, Scattered Weapons, and Danger Zones in combat challenges so that you can relax in the predator maps. Protective Auras and One Hand Tied are best used in predator challenges. For the beneficial mods, generally you will take Super Powered on the more problematic combat maps, Knockout Projectiles on predator maps, and Free Medal to avoid annoying predator medals that require positioning more than one goon. Make sure that a mod does not prevent you from getting a certain takedown for a predator medal, One Hand Tied is the only one that comes to mind.
Recommended mods for the last two:
Scare Tactics (Predator Master)
--Breaking In: Time Limit, Protective Auras, Scattered Weapons
The time limit is no big deal, just watch for the mines when you go for the window takedown and the tightrope takedown. There aren't a lot of good vantage points for Fall Guy, so glide onto the file cabinet thing early and get that out of the way
--Wrecking Crew: Danger Zones, Free Medal
I used the free medal here to avoid dealing with Scare Tactics. Danger zones is no big deal since there are plenty of floor grates to hide and move around in. If you need vantage, you can always string a tightrope up between the gargoyles. Just jam the last guy, let him try to shoot, and then beat him down.
--Hard Time: Increased Agression
Keep one unarmored guy conscious, he will eventually take the hostage and you can get above him and get Smash Landing to finish the map. You can use the sonic shock whenever, you don't really need sonic batarangs here. This map has great spots for batclaw ledge takedowns, just stand on the little roofs in the corners and pull people off the central walkways. If you are lucky, you will even get credit for the batclaw disarm this way.
Standing Count (Combat Master)
--25 to Life: Protective Aura, One Hand Tied, Decreased Health
I like to get Protective Aura out of the way first because it is somewhat annoying. One Hand Tied actually synergizes well with it here, since special moves are a good way to break your combo with an aura in the fight, and you will need to farm combo and shock glove charge on the armored goons (just start a beatdown and interrupt it with a counter whenever you can). If you are ever in question about the aura status of an offscreen enemy, just evade towards them (redirects won't break your combo even after two) until you can see clearly.
--Death Sentence: Scattered Weapons, Gadget Malfunction.
Gadget malfunction is no big deal here since it is very easy to keep your shock gloves up, lots of armored or special enemies to beat down. For the big guy, instead of evading over his head while beating him down like you would in arkham city, try using bat swarm every time it comes up. This is to avoid any silliness from the martial artists. When your gloves are up, prioritize the martial artists.
--Panopticon: Super Powered
This is your victory lap, go nuts. By the way, a panopticon is a place from where you can see everything. Pan + Optic