You can easily glitch your way to any level … starting after you first leave the vault.
First, travel to Megaton and speak to Walter. Find and repair the three leaks around town (Crimson Drifter
has pointed out that you must have a Repair Skill of 30 or higher to fix the Megaton leaks). If you like, feel free to complete “Power of the Atom” (if you do, you MUST disarm the bomb). Sell most of the things you carry … except for some weapons and ammo.
Second, collect any scrap metal you find, as much as you can carry (so long as it is an even amount). The more you have for the next part, the better. Additionally, through your search for scrap metal and the locations necessary, try to stay neutral or good, and allocate any points awarded from leveling up into sneaking.
Some decent places to gather scrap metal are the Robco Factory (located south-west of Megaton) and a wandering seller named Tinker Joe who occasionally appears outside Robco, as well as the Meresti Train Station (where you find the Family in “Blood Ties”).
Next, make your way to Fort Independence and look for Protector Casdin. You can sell this guy your scrap metal 2 pieces at a time. This is where the glitch begins. To save frustration, save after every step. For the sake of argument, I will use 48 pieces of scrap metal as an example.
Step one: Sell every piece of scrap metal you have on you. (48 pieces)
Step two: Pick his pocket and steal it all back. DO NOT GET CAUGHT.
Step three: Sell all but 2 pieces of scrap metal back to him. (46 pieces)
Step four: Again, pick his pocket and steal all of the scrap metal back, in addition to his rifle. HE SHOULD CATCH YOU (and hopefully not attack you) AND TAKE ALL OF YOUR SCRAP METAL AWAY.
Technically, though it doesn’t appear in your inventory, you have unlimited scrap metal (provided you got the glitch to work). DO NOT pick up any more scrap metal, or it will end the glitch.
Immediately, head to Megaton and see your pal Walter. Sell him all of your scrap metal, which awards you XP, and you can repeat the transaction as many times as you wish until you level up to your desired level. STOP AT THE LEVEL PRIOR TO THE LEVEL NEEDED FOR THE ACHIEVEMENT.
Now, make a few saves for evil, neutral, and good. Depending on your current status, you will need to either gain positive karma or negative karma.
Negative karma is easy to attain. Murder townsfolk (DO NOT MURDER WALTER) and steal things.
Positive karma is a little harder to attain. You can donate to the churches in Megaton or Rivet City (provided you did not kill the priests) or give your purified water to the beggars outside of Megaton and Rivet City. If you have the house in Megaton, Wadsworth will give you some purified water.
Return to Walter in Megaton after reaching your desired karma and sell more scrap metal to level up once more to unlock the achievement. Continue to level up for the remaining karma/level based achievements. Load the other saves to pursue the other karma options.
EDIT: WHEN / IF CASDIN ATTACKS:
Sometimes when you try to pick Casdin's pocket at Fort Independence and steal back your scrap metal, he will attack you. This doesn't always happen ... but if it does, one or more of the following may remedy the situation (all according to research and/or trial and error):
1) Some suggest if you have open quests he will attack. I cannot confirm or deny this, but it seems ludicrous.
2) Some suggest if you do not have enough rep with the Outcasts he will attack. Credit to Antonysj
who had this problem and his solution was to "[give] him some power armour and laser rifles, this was slow so I just went to the alien crash site and salvaged the alien blaster and ammo and gave that to him, instantly making him trust you. You can then pick the alien ammo back, and (providing you have the Broken Steel DLC) get another alien blaster later." Thank you, Ant, for providing a tried and true solution.
3) Some suggest that you do not attempt this glitch at too high a level ... I have no idea why.
4) Some suggest to steal the key in Casdin's possession rather than his rifle ... there are reports of players not being attacked, yet still being caught, while stealing the key. IIRC, my character had to steal everything in Casdin's possession in order to be caught, and I was lucky to not be attacked.
5) Some suggest that if you have previously met and killed off any Outcasts prior to attempting this glitch, Casdin will attack ... which makes sense.
6) Some suggest that karma is key ... if you're good, you're golden; if you're a bad boy, forget about it.
7) Finally, some suggest that your CHA stat will influence whether or not Casdin will attack ... the higher your charisma, the better your odds, and if it is below 4 or 5 you can forget about success ... which makes sense because your charisma determines how people react to your character.
What I suggest:
First, try and steal the key and see if that works for you. If not, well, you have a plethora of options. Examine your karma and CHA and see if you can improve them. Think back to any random people you killed .... were they Outcasts? ... and you can always do like Ant did and fork over some power armor and laser rifles to improve Casdin's disposition towards you.
If those seem to fail you, revert to an earlier save ... which could mean a "right-out-of-the-vault" save, and follow my guide to the letter. If that fails, well, I hate to be the bearer of bad news, but some people online have even said they have had to start a new game completely ... which basically means you would have to play through the vault again. In any instance, whichever course of action you decide, be sure to allocate those points and perks into things that will aid you in this specific task ... charisma, sneak, stealing, strength (the more scrap you can carry, the better!), etc.