Um...I guess you can clear Dreadfall ahead of schedule. I've never tried.
In theory, you can take your level 1 character straight into Dreadfell and start blasting away. There is no prerequisite for entering. All of the "main plot" quests start there; anything you do before that is just warm-up.
In practice, if you actually want to try for that achievement (I'm not talented or insane enough...) you'd probably want to kill everything except the bosses in every other dungeon, for the experience points. You could also hunt adventurer parties (and good luck not dying).