The Batclaw in Predator rooms. A single use of the Batclaw on a mook next to a railing will result in an automatic takedown, as the mook is pulled over the railing and falls to the ground. This removes the risk of Batman being spotted and getting shot at due to the range of the Batclaw's rope. All of the Predator rooms from the point where you acquire the Batclaw have such railings. The Ultra Batclaw will allow you to pull up to 3 mooks for an instant takedown, but there's only one predator room left in the story when you get it so it doesn't get to be as useful outside the Challenge Mode.
While there aren't really any for the main game, Bat Swarm is extremely handy in Combat Challenges; it gets everyone off of you, can get you a few thousand points if your combo is high enough, and makes the Lieutenants a piece of cake (do the move close to them, pummel them to get your combo gold again, then do it again as they start to recover).
Not full-on game breaker, but damn close: the Batarang Takedown. When executed, any enemy that's been knocked to the ground gets pelted in the head and instantly knocked out. It makes you feel like a total badass to instantly neutralize seven or eight mooks with one move.
The secret to breaking combat challenges is Redirect. The AI can't handle it well. Literally just attack once, redirect, repeat. It overrides attacks that could be countered, knife attacks that have to be dodged 3x, titans, everything. Throw in the occasional takedown for armored enemies but as long as you remember to redirect after every attack you will get 60-70ks in no time. Getting larger comboes gives better multipliers.
All combat challenges become a breeze after one acquires the Shock Gloves. Once activated, they can punch through any measly defence that the mooks might have, and they double the hits in the combo counter, making it easier to pull off special combo moves. In addition, some campaigns allow you to use an ability that allows you to punch through shields, armor and batons, like in Arkham City. The difference here is that instead of just doing that, the power-up simply gives you infinite shock glove use during the fight. Combine that with the shock glove's multiplier effect, and it's not that hard to get triple the points needed to get all medals on that challenge.
The Shock Gloves also allow the player to string two special combo moves together. Once the Power Gadgets upgrade is unlocked, fights become as simple as building up the two moves, and using the powered Explosive Gel, followed up by the Multi-Ground Takedown.
A big deal was made about how hard the I Am the Night -mode was going to be, since the player has only one life to beat the game with no saves... except the developers forgot the last part, and the player can use the restart feature between checkpoints with no repercussions as long as they don't die.
The Remote Claw in the predator sections allows you to take out any unarmored henchman that so much as wanders near a gargoyle or other vantage point from a distance. Since they're everywhere, they make those sections a lot easier than they really should be. To top it off, you can farm enough EXP to fully upgrade the claw before entering the GCPD.
If you're ever overwhelmed by groups of thugs in the streets, the Enhanced Dive Bomb makes it insanely easy to whittle down forces. Dive Bomb, grapple away, repeat. You can even use the glue mine for ensured multiple knockouts.
Fully upgraded smoke bombs and glue grenades. You can take out entire predator rooms by first tossing a smoke bomb into a group of enemies, gliding in and spamming Quickfire Glue Grenade > Takedown . This works on every enemy type, and only those with night-vision goggles can stop you (so make sure you attack them first).
The disruptor rifle. With the right upgrades, you can use it to sabotage virtually any piece of enemy equipment, from medic backpacks and detective mode trackers to weapon crates and deployable sentry guns. This typically results in the equipment taking out the user when they try to use it. You can literally take out up to four enemies without so much as touching them and render Medics useless in both fights and predator sections, and the enemies have no countermeasures whatsoever. Though these upgrades don't show up until after you first deal with them (showing Batman being Crazy-Prepared) and can be more of a cathartic factor to some players after having a pain dealing with them. Plus, using the disruptor will highlight enemy equipment, providing an alternative to Detective mode for encounters with the DM trackers.
Quickfire batarang + multi ground takedown = at least 3 enemies knocked out after every 5 hits.