Common sense but not many know, during the "Fate, Up Against Your Will" (This is alliance only) You are put into Orgimmar with no hostiles in the area. This is your opportunity to run around without worrying about guards or horde. This is the perfect opportunity for us those don't have stealth to enter Ragefire Chasm to get the achievement.
Did a quick search. Terribly sorry if this is a repost.