Just finish the story and you will unlock New Game +. Choose it at the start screen and just run through the game once again. If you have all the other non story related achievements, you can finish it in about 90 minutes. Don't try to kill enemies unless you really want to and only fight when you have to defeat someone for the level to progress.
If you didn't get one of the achievements on you first run, just do it here. Everything will carry over except for a few Vigils like the one for doing the seven challenges. So it's better to finish those off on your first run.