This problem has different solutions depending on how you want to play.
If you're just looking for the achievement, one solution to your problem is to do whatever missions you want, choosing the side of good, until you get relatively close to your level point. Then go into a town and steal (for minor karmic reduction) or lay waste to entire towns (for major karmic reduction). You can quickly lower your karma this way. Then, once you're neutral, go kill some random creatures until you level.
(If you're looking to steal, a good place to do it is at Dukov's place… he's got stuff everywhere.)
The "nice" thing about this system is that if you stay on the path of "good" the whole time, you can do this at each achievement point: be bad until you get to the right karmic level, level up, get your achievement, and then restore a save to get back to your good self. You can quickly get "good", "neutral", and "evil" achievements for all levels on one playthrough this way.
(I did this, because I don't really enjoy long-term playing as an evil character… but I do like my achievements!)
You could also do this as an evil or neutral character, but it's much easier to quickly drop from "good" down to your new goal, than to work your way up.
If you find that you're close to leveling, and you're at the right karmic level, and don't want to take a chance on changing your Karma by doing a story-type adventure, you can always go wandering looking for random bad people to take out. Going near the Washington Mall can get you some XP fairly quickly, and you can go inside the capitol building and clear out large areas without picking up any Karma, positive or negative.
The moves you have to perform in a single combo are (PS3 / 360 / PC):
Strike (Square / X / Mouse Left)
Counter (Triangle / Y / Mouse Right)
Cape Stun (Circle / B / Mouse Middle)
Evade (X x2 / A x2 / Space x2)
Throw (Square + X / A + X / Shift + Mouse Left)
Takedown (Triangle + Circle / B + Y / Shift + Mouse Right)
Ground Takedown (R2 + Triangle / RT + Y / Ctrl Left + Mouse Right)
Batarang (L1 / LT / Q)
Batclaw (R2 x2 / RT x2 / C)
As far as which order and where to do it, I would check sites like True Achievements (Xbox 360), or PS3 Trophies Forums for some tips. Check YouTube as well, there's loads of videos for it and a bunch of different possible solutions.
Best Answer
Basic Moves
Evade 360: (Ⓐ,Ⓐ) PS3: (✕, ✕)
Strike 360: (Ⓧ) PS3: (□)
Counter 360: (ⓨ) PS3: (△)
Stun 360: (Ⓑ) PS3: (◯)
Ultra Stun 360: (Ⓑ,Ⓑ,Ⓑ) PS3: (◯,◯,◯)
Aerial Attack (Ⓑ,Ⓐ,Ⓐ+↑ forward) PS3: (◯,✕,✕+↑ forward)
Combos
Special Combo Bat Swarm 360: (Ⓐ+✕) PS3: (□+✕)
Combo Batarang 360: (tap LT) PS3: (tap L1)
Finishers
Special Combo Takedown 360: (Ⓑ+ⓨ) PS3: (△+◯)
Beat Down Finisher 360: (Ⓑ, ✕repeatedly) PS3: (◯,□ repeatedly)
Good places to complete this are the Survival of the Fittest Challenge Map or on the Joker's Carnival DLC Map (if you have that available to you). You should definitely get as many combat upgrades as possible, or at the very least, get the Special Combo Boost and Freeflow Focus upgrades. Critical Strikes will also help build your multiplier faster.
Credit goes to Xbox 360 Achievements for the listing!