Since there is no guide for this one, I'll give it a shot.
The campaigns consist of doing 3 maps in a row from the normal section, but you only have 3 retries before you have to start over. You also have buffs and debuffs that are given for each campaign, all of which have to be utilized by the time you finish. In other words, if there are six total modifiers, and you use a total of four on the first two maps, you will be forced to use the last two on the final map. For this reason, it is imperative that you plan out what you're going to do.
1) I would recommend getting good enough at the combat challenges that you can get 3 medals without much difficultly. The predator maps will often be the harder parts of the campaign, as you can quite easily miss a specific type of takedown or get shot to bits if you get careless.
2) Use as many debuffs on the first map as you can. The first map is repeatable, and you can therefore try as many times as you want, so you're going to want this map to be your most challenging. Don't be afraid to fail a couple times if it means smooth sailing for the rest of the campaign
3) I recommend doing this achievement at the same time you are doing the regular ranked gold achievement. In particular, as soon as you figure out how to do a predator map, go right over to the campaign with the corresponding map while you are still familiar with it. Predator requires knowing what you're doing (especially on the final maps) and you're gonna want your path fresh in your mind.
4) Be aware of which buffs/debuffs are good for which game type, but also be aware if a debuff will prevent you from completing a predator task. For example, if you're on the third map of your campaign, and you are required to do an inverted takedown from a gargoyle, but you are stuck having the gargoyles booby trapped, then you're shit out of luck. Plan ahead.
5) If a map starts off badly, resist the urge to hit restart if you're not on your first map. I know this is obvious, but I quite frequently hit it in frustration only to remember a second too late that restarts aren't free.
A list of buffs/debuffs and my opinions on them:
Gadget Malfunction: In Combat, all gadgets will be disabled. In Predator, Detective Mode will be scrambled for the entire challenge.
Opinion: This one is obviously best saved for combat. It’s not a particularly bad one either. Just don’t forget it’s turned on.
Time Limit: Adds a time limit to complete the challenge. Defeat enemies to extend your time.
Opinion: This one can be used on either Combat or Predator depending on your confidence in your ability to beat a predator map quickly. Though, it’s pretty hard to fail on a Combat challenge if you are consistently killing guys using special takedowns, etc.
Increased Aggression: Enemies will be stronger, faster and tougher!
Opinion: I never noticed much of a difference in either scenario. I assume you have less time to react in Combat to counters and they take more damage. In predator, I believe they are more aware and their guns do more damage.
Decreased Health: The player starts the challenge with reduced health.
Opinion: In predator, you start with almost zero health, while in Combat, you have more of a cushion. Best saved for combat unless you’re confident that the guards won’t even know what hit them in Predator.
Protective Aura: One enemy will be surrounded with a protective aura which prevents them from taking damage. The aura moves from enemy to enemy over time.
Opinion: This one is annoying in both modes. In Combat, if you try to attack him, and he’s the only one around, you lose your combo. In Predator, it can make a guy immune just as he gets right next to the glass or wood or whatever. Either way, best taken care of on the first map if you can.
Danger Zones: In Combat, Gun Racks will be activated during the challenge for enemies to obtain firearms. In Predator, the environment will have booby-trapped Vantage Points.
Opinion: I live on the Vantage Point gargoyles, and I assume most other people do too. Not to mention, they are a must if you need to grapple out of a sticky situation. For most people, I would think this is best saved for Combat, but that depends on your play style. Unfortunately, this debuff is on the Predator expert campaign (the last one). I saved it for the last map and used the room with the sniper across from your spawn as a vantage point to knock guys off edges with my REC (in case you were wondering).
One Hand Tied: In Combat, counter icons will not be displayed before an enemy attacks. In Predator, the player will not be able to perform a Silent Takedown from behind.
Opinion: Both of these options are bad and depend on your play style. If you’ve beaten New Game +, you should be relatively comfortable countering without icons. However, some people don’t use silent takedowns from behind, so it’s really up to you. This one is best used on the first map though, as it can really throw you off.
Scattered Weapons: In Combat, enemies will pick up and throw objects at you. In Predator, the environment will start pre-mined with proximity activated explosives.
Opinion: While the thrown objects aren’t a huge deal, the pre-mined predator maps can actually be a buff. You can use your disrupter early in the round to take out guys standing next to them to thin their numbers. You can also use them to draw attention if your sonic batarang is on cooldown. Just remember they are there, because you may quite often run over them while trying to escape.
Replenishing Health: The player will slowly regain lost health over time.
Opinion: Best used in Predator, as you can take all the time you need to regain all your health. Also, if you’re dying in Combat, you’re probably not getting all three medals.
Takedown Projectiles: Upgrades your primary projectile weapon to knock out enemies with a single hit when thrown with the Quickfire button.
Opinion: I never used this one myself. I would just advise that you remember that they have to be quickfired and that doing a ton of damage isn’t always a good thing in Combat if you’re trying to build up your combo.
Super Powered: Gain the ability to punch through Shields, Armor, and Tasers without getting blocked. In Predator, you will move faster when crouched.
Opinion: This one is most definitely best used in Combat. While crouch walking faster is good I suppose, not having to worry about shields, etc. makes it so much easier to keep your combo going.
Free Medal: yo, Free Medal, yo.
Opinion: Never use this on the first map. I like to save it for tricky Predator medals, particularly for “Don’t Touch That Dial” which prevents you from killing the jammer guy until last. With this active, you can off that guy and get your predator vision back immediately. It’s also good for when the bastards refuse to wander over close to windows or walls.
Well, that’s all I can think of. If you guys have anything else you want me to add to the guide or want combat tips or whatever, let me know.
For more specifics to the Predator Extreme guide, see G C Squared solution below.