** MINOR SPOILERS BELOW. **
To get this achievement, you need to reach level 20 with bad karma.
Getting to level 20
Straightforward enough, but there are ways to achieve this more quickly. First, avoid companions.
Second, look out for the NPCs who request certain types of items, and then watch to see if redeeming those items provides XP. Two such "standing orders":
* Scrap metal in Megaton. (Easy to find everywhere.)
* Pre-war books at the Arlington Library. (Excellent per-book XP.)
Lastly, I recommend hacking every terminal, picking every lock, and attempting (almost) every speech challenge. All provide nearly guaranteed XP, without the hassle of a fight.
Bad karma is easily obtained throughout the game, usually through the theft of items or the murder of wastelanders, but can also be gained by simply being mean during conversations. (I particularly enjoyed making children cry whenever possible.)
If you have a good/neutral karma and need to decrease your karma, this is easy -- go on a killing spree in Megaton or Rivet City. (Megaton is great for using the Fat Man.) This will have some obvious gameplay effects (reduced numbers of merchants to access), however, so I suggest saving the game prior to this -- go get the achievement, load your save, and then continue.
Neutral karma can be a tough target to hit sometimes, so my suggestion is to check your karma after each murder / mini-nuke. Once you hit neutral karma, simply stop killing and run away until you are out of range of all angry wastelanders.
If you actually need even more karma loss than that, first steal everything you see, but be careful not to be caught, as it will typically provoke a gunfight. Then go on your murder spree.
One last note: Taking the evil path during the Power of the Atom quest will provide a lot of bad karma, so feel free to save that quest for "the right time".