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.
I believe most, if not all, of the accumulative achievements are tracked across multiple playthroughs. Like the moose finding achievement, I know I have been using several playthroughs trying to get that and so far it has tracked my progress accross all of them.
Best Answer
Once you complete a part of the story, at any time, you can go back and hop around to get the various achievements. The problem is: What do you define as a 'playthrough'? If you are looking to estimate the time it would take, due to the random nature of dungeon and event generation and positioning, this is a flawed metric.
If you consider a base definition of a playthrough as playing from the start of act 1 to the end of act 4 sequentially, not accounting for re-instancing the areas to farm dungeons, drops and events, the absolute minimum would be 4 runs for each of the 10 characters on each difficulty, assuming everything worked out perfectly and you found all the random stuff and all your characters leveled to 60, making for a total of 40 playthroughs, with at least 4 of these being hardcore on each of the difficulties and at least 5 of these being multiplayer, playing each class at least once and each difficulty at least once.