This achievement requires you to experience 4 different endings in the game. Each one differs in how the Archdemon dies, and who dies with it, or doesn't.
Ending 1 - Choose Morrigans way out and sacrifice no one to the archdemon.
Ending 2 - Turn down Morrigan (she leaves your group) and sacrifice yourself to kill the archdemon.
Ending 3 - Turn Down Morrigan, and let Allistair kill the Archdemon.
Ending 4 - Turn Loghain into a Grey Warden at the Landsmeet (Allistair will leave your party) and at the final battle choose him to kill the Archdemon.
Technically these take 4 playthroughs to accomplish, but for those of us without 160 or so spare hours to slog through the same missions four times, with careful saves you can easily get this with one character, and about 2-3 hours depending on your difficulty.
Save 1 - Once you reach the Landsmeet, make one new save before entering the Landsmeet Chamber. This save will allow you to go back and choose who you pick. Once inside, it does not matter who you choose, Allistair or Loghain. Each is only required for 1 of the endings, and you can get the other 3 with either one. You don't even need one of them if your character is male (for Ending 1).
For this guide I picked Loghain as Allistair was in love with my Character, and would, if in the party at the end, not let her sacrafice herself to slay the archdemon.
Save 2 - Next, once you get to Redcliffe castle and after conversing with the Arl and the others, you will have to go upstairs to talk with Riordan. Save either before conversing with him, or right after. Make sure NOT TO GO INTO YOUR ROOM BEFORE MAKING A NEW SAVE. Once in your room Morrigan will make her offer to you. Choose to not take her offer this first time.
Save 3 - Finally, once you get to the final battle, and after taking back the gates, make one more save before you talk to Riordan. This save is how you choose who goes with you to the Archdemon, as I said if Allistair likes you enough he will not let you sacrifice yourself. And as for Loghain, I have not tried taking him and choosing myself to do the slaying. I do not know if he will let you do it or not, but once again I suggest saving here just in case.
Now you have all the saves you need. If you have followed this guide to the letter so far, then i suggest NOT taking any other Grey Wardens to the Archdemon, and sacrificing yourself at the end getting Ending 2. Next go back to the Save 3 and take another Grey Warden with you, whoever you picked at landsmeet. Sacrifice them to the Archdemon, getting Ending 3 or 4.
Next go to Save 2, and pick Morrigans offer with whoever you have, or yourself if your character is male. This will get you Ending 1. Finally head back to Save 1, and choose the opposite character as you did the first time, and play till the end, turning down Morrigans offer, and choosing to sacrafice them at the end.
I do not know for sure how the have it setup to check the conditions required to unlock the achievement, either checking all saves, or your profile itself, I do not know. So i suggest viewing the ending, and making a new save after each ending. It takes an extra 5 minutes if you use X to skip everything, and means 4 more saves, but it with all this work already, it is worth it.