To get all of these in a single playthrough, you will need to make sure you save your game at levels 7, 13 and 19 and do all three of them before moving on and before saving over your old save file. Also be sure to save a side-quest or main quest for just before reaching each of the required levels to make it easier.
I would suggest being good at first. Getting bad karma is the easiest, so staying good the entire game will make it easier to handle these. Get your achievement for good, then reload your save. Go on a murder spree until you hit neutral, then turn in your quest to reach your target level. Reload your save yet again. Go on an even bigger murder spree until you hit bad, then turn in your quest to reach the target level. Repeat this process for each set of achievements.
Note: See "Silver-tongued Devil" for a few infinite speech challenge loops. You will gain experience for every speech challenge won, so these will also aid in getting to the level you need without messing up your karma situation.
Note for PC Users: I would suggest just playing the entire game out once being either good or bad as these sets of achievements can be done in about 30 seconds each. Start a new game and while you are looking at your father in his scrubs, go ahead and open the command console and type "player.setlevel 8"and this will grant you the neutral level 8 achievement. Open the console again and type "player.setlevel 14" and finally "player.setlevel 20" for all three neutral achievements. Quit out and start another new game. Open the console and type either "rewardKarma 1000" or "rewardKarma -1000" to get to good or bad karma, depending on which one you still need. Repeat the steps for using the commands to obtain levels 8, 14 and 20 for the last set of achievements.