This is currently one of the three least unlocked achievements, along with the "Lord of Murder" and "Worst Day Ever" achievements. It's a bit time consuming, but can be done in a few hours. Here's how:
Start a new game in Shadows of Amn, and choose Story Mode for your difficulty. You can make any sort of character, but I suggest a Fighter or Paladin for ease. But you might also consider choosing a class for which you need to unlock the "level 30 class" or stronghold achievement.
As the game starts, Imoen will join the party - you can't stop that from happening. Just immediately remove her from the party as soon as she's done talking, and you're good to go. (I believe it's her XP amount that counts. Either way, this is the only way to do it.)
Now just play through the game. Don't worry to much about equipment, but get something decent. Mostly just use stuff you find or receive. Of most importance is having a decent weapon, to overcome enemy defenses.
Because you're playing on Story Mode, you're invulnerable, and can just run into battles without thinking too much about it. In fact, you can just let the AI take care of that if you want to.
Make sure to never add any other member into the party! So whenever some NPC with a portrait comes up and talks to you, be sure to click the correct responses so that they don't join.
Avoid too many side quests. Just go for the main storyline. You might also want to do your character's "level 30 class" or stronghold achievements in this run though, in which case the stronghold quest and maybe a couple others can be a good idea. You'll probably reach level 30(or almost that) from the XP of the final boss fight though, and any remaining levels to 30 can be done in Throne of Bhaal.
And that's pretty much it. Just run through the game. I think this took me about five hours or so, but it's possible to play through the game in just a couple of hours(or even less) if you know very well what you're doing.
Anyway, after defeating Irenicus in hell and watching the final cutscene, the achievement should unlock! And if you hadn't already unlocked it, the achievement "Friend of Volo" will also unlock for completing the game in Story Mode!
Note 1: Unless you're playing a caster with access to Wizard spells, you might not have access to identifying outside of shops. But most equipment can be equipped and used without being identified.
Note 2: Getting money shouldn't be too big of a hindrance, as you'll be selling most of the magic items and other stuff you'll pick up anyway. Since you don't have to worry about equipment for other party members, this actually heavily affects the amount of gold you get. I actually bought the Shield of Balduran almost immediately after getting through the prologue, and that shield costs 15k!
Note 3: Getting the "Paws of the Cheetah" boots can be a really good idea, as it will make the entire rest of the game go that much quicker. You can get them early by doing either the Thief or Bard stronghold quests, though the former requires you to be a Thief yourself. Or you can just kill Renal Bloodscalp in the Shadow Thieves' Guild Hall and take his boots.