(Semi-Copied over from "Last, Best Hope of Humanity")
The best advice I can offer for this achievement is to play the game Good, as it is much easier to get Bad Karma then Good Karma. When you get to Level 7, you can get the other two achievements, "Mercenary" (Level 8 Neutral) and "Reaver" (Level 8 Bad), as well.
Upon reaching level 7, you can either get more XP until you are just on the brink of Level 8 or you can play it safe, save at the start of the level, and work towards 8 and each side of karma.
To get karma, here are some tips:
For Good karma, give Purified Water to the tramp outside of Megaton. He will be to the right laying on some rocks just outside the gate. You can get purified water from Wadsworth at your house. (NOTE: You will only have a house if you have completed "The Power of the Atom".)
For Bad karma, well... this one is easy! Murder, steal, massacre, hit people, whatever you want to do.
A friend of mine recommended saving the "Power of the Atom" quest until you reach one of the levels before those in the achievement (7, 13, 19). Once you get to the level, either blow up the bomb or disarm it, and depending on which, you will get XP and karma for completing the quest. The one problem with this is that you might not have Tenpenny Tower in order to blow the bomb up at level 7.