You can get both this achievement and the one for maximum positive reputation in the same playthrough. One is based on the positive bar, one is on the negative, and you can raise both bars simultaneously. (That's weird, but whatever.)
I'll assume you've been working on the positive reputation. Once you have that, back up your save, then go on a killing spree. I did this late in the game, so I knocked out a couple of factions at the same time. I had brokered peace in Stellar Bay, so I went through and killed EVERYONE. Then I went to the Groundbreaker and started killing everyone.
I didn't get to 100%, but they were at least 70% negative or so. (I can't remember exactly what I got because I reloaded the save right afterward.) Then you can reload to before the slaughter and continue with your game.
So no, you don't have to play twice for this.
Hope this helps!