Fur, Feathers, and Fists

Since launch, Rocksteady has released several Crime Fighter packs with various challenge missions for most of the playable characters. Unfortunately, Harley Quinn, and Red Hood haven't received any challenge maps specifically for them, but due to the addon allowing for all fighters to be used in most maps, this is of little concern.

  Jason asked nicely 

     For this run down I will be working under the assumption you are playing as the character intended for the map, if you find it easier or harder playing a map meant for Robin as Nightwing then go ahead.

Shark Bait

Don't call him a sidekick 

Play as the original Robin (so Nightwing) at Bludhaven docks in a four round death match. Remember as Dick you have the REC, batarang-like escrima throw, electric pulse, and grapple at your disposal. Your two special moves, aside from the takedown, are the multi-shock, and escrima flurry. Both basically strike opponents around you so try to use them in the middle of a group. The first two rounds are pretty simple. The last two have two big guys, and the last has a bunch of stun sticks. You'd think Dick would have gotten Bruce to teach him how to destroy those. Remember the basics of combat maps from earlier to help, and especially try to get a flawless combo in at least the first two rounds.

Scales of Justice

"He's just a kid!" - Guy who was just beaten up by a kid

     Robin's turn. Same as before, four rounds, but in Two-Face's "Courthouse". Robin has grapple, his shield bash, snap flash (like the explosive gel), and birdarang. His specials are a throw (not very useful, but its a variation bonus), and a spin with his staff. Robin has a lot of variation so make sure to take advantage of it. Ok this one seems to have less "dangerous" baddies. Remember you can use the instant takedown on one of the big guys if you need, but try to do the beatdown on one as the hit counter will go crazy. Also listen for the audio clues for a thug going for the gun case, like Nightwing, Tim lacks the Disarm and Destroy move so if one gets onto the field you can't take it out.  

Destruction Line

Selena returns to Riddler's factory for this challenge. Unlike the previous ones, there are no big enemies. I guess all of the freakishly large thugs in Gotham were taken. But there is a unique twist in this map; environmental hazards. Round two sees the walls become electrified. You can use this to your advantage by sending thugs flying into them for a takedown. The next round starts lasers that move randomly across the field. These will be your biggest danger. Remember, Selena only has her whip, bolas, and caltrops (three for the whole challenge, so use wisely). Also the bolas are mapped to square, and her whip, which is slower, is on the batarang button. Her specials are mirrors of Nightwings. In Round three a thug with a gun spawns, so watch out. 

Clockwork

The Dark Knight returns in this map in Barbara's Tower. Space is tight, and the marks for each star are lower, but there are also less thugs. You need to maximize your variation and not get caught up just punching everyone. If you're looking for that last bit of variation bonus to squeeze out of Batman, don't forget the freeze grenade, I...may or may not sometimes. In the last round there are two big guys, several stun sticks, and a gun. Be careful where you target, and use Disarm and Destroy, finally someone who has it.

Try not to get blood on Barb's floor

Wild Cat

Get ready to go wild as Catwoman on the western set in the Panessa movie studio. This is a timed challenge with you having to acquire as high a score as possible in the time limit. Each takedown will give you a tiny bonus to time so try to focus on taking out thugs as quickly as you can. Also the gadget and move variation bonus's still apply so make sure you try and use everything at least once. While it might be tempting to use the takedown special, it can end up having a long animation that burns lots of the clock. Similarly, Selena's aerial move (stun + dodge) has a long animate. Keep in mind that her beatdown, and Whip Trip are both fairly quick, and effective. Also thankfully you will only find normal enemies armed with just bats (the club, not the Knight) and knives. Try to use the blade dodge takedown as much as you can to maximize your efficiency. 

Quarantine

Teach the militia in Ace Chemicals that Batman isn't the only one they need to worry about. This challenge brings in the new medic enemy. Most of the rounds will have at least two of them. You can either target them first, or try to use them. You can let the medics heal soldiers to try and milk the round for more points. Remember, the electrical charge they can give thugs gets dissipated by most of your gadgets. Another thing to keep in mind is that when you are doing a beatdown on a target try to angle the camera so you can see the enemies around you, some bad guys have deceptive range that might make you miss the wind up if you're not careful. Also the last round is VERY dangerous, with multiple gun-armed thugs, armored guys, medics, and combat experts (the ninjas). 

Guardians

Seriously! Why are you a criminal if theres a crazy crime-fighter who can do this?!

The original Dynamic Duo are back defending Panessa Studios from evil. This Duel Play challenge features a timer, so efficiency is the name of the game. Try to avoid the awesome duel takedowns as they add time (with style at least). One bonus is that you can add lots of variation bonus with both of their moves. This one should be fairly easy to 3 star.

Precinct

This challenge sees Robin taking down Penguin's goons in the GCPD parking area. The enemies are fairly basic with just a handful of stun stick and big guys to give you trouble. No real need to worry about this one. 

High Interest

Own the skies with Batman. This is a difficult challenge not just because of what they throw at you, but how they do it. There are no rounds, just a series of spawning waves so you need to make each hit count. You will have to face big enemies, combat experts, shields, stunsticks, and guns, both spawning and from boxes. Also there will be junk littered around that thugs will try to throw at you, so keep an eye out for those, especially look for the propane tanks you can use to finish an unlucky guy off with. There are also some environmental takedown areas to exploit in the corners. 

Flying Grayson

Why do people mess with these heroes again?

This is another Nightwing map. Fight an endless wave of thugs in the Arkham Knight's underground base. The tip here is to last as long as you can. With practice it should be fairly easy to last long enough to get the three stars. Guns WILL spawn so keep an eye out for bad guy's loading so you can stop them. Also if the big guys are giving your trouble you can just save your special moves for them. Ultimately, just remember that this is a losing battle from the beginning. Don't sweat losing your streak. 

Feline Frenzy

Another fight till you die with Catwoman this time. This one adds medics to the mix, and while their reviving won't really matter here, the electrical field will so watch out. Unfortunately, without Disarm and Destroy you will just have to use all of your gadgets and moves than last as long as you can. 

Assault on GCPD

The new Dynamic Duo defend GCPD from the militia. This is the same as with Nightwing, but no time limit. Just switch between the two, hitting as many of each hero's variations as you can, and try to get the flawless bonuses. 

Newton's Cradle

Another combat time trial, this time with Nightwing. Same basic principle, as you fight tougher enemies will spawn. Eventually you will have to contend with guns, stun sticks, and giants. Again not as hard of one to win.

Two for the price of one

Cat's Conundrum

This is actually a fairly unique challenge map that should seem familiar to anyone who has played at least part of the Riddler/Catwoman story in the game. You play as Selena and fight waves of Riddlerbots, of both blue and red varieties. The catch, you can only hurt red ones, but can toggle the colors by moving through platforms on each wall. This map will test your ability to precisely target enemies. You can try to keep streaks going as long as you can, but eventually you will have to break it to switch all of the bots to the right color. 

Teen Titan

CATCH!

Finally its Robin's turn in an endless bad guy beatdown. Its the same drill as before, fight till you die. After awhile the center will be a sea of different enemies, it makes Robin's Staff Spin pretty fun to use. They will throw pretty hard enemy types, like the armored shield guy, pretty early, but it isn't too hard of a challenge.