** MINOR SPOILERS BELOW. **
To get this achievement, you need to reach level 20 with neutral 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.
Karma
Neutral karma generally means that you do as much harm as good. Playing through the storyline as the traditional hero will get you a wealth of positive karma, so getting the neutral karma achievements will require you to do some evil (mostly murder and theft).
If you need a karma boost, I have two suggestions:
* At the Church of the Atom (Megaton) or Saint Monica's Church (Rivet City), donate caps. If you have a lot of cash lying around, it will be very easy and quick to get into "positive" karma.
* In Megaton, give away your scrap metal rather than requesting payment. (You still get the XP.)
If you 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 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, 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.