Solo run of Zul'Farrak for the achievement. If all you're going for is the achievement for completing the dungeon you can skip a few bosses. This instance is meant for level 43-46 players and is located in the north-western corner of Tanaris.
Solo run of Uldaman. This wasn't always possible to run solo. Originally you needed three people to use the Altar of the Keepers which made doing this instance a pain. I'm not sure when Blizzard changed this but I'm glad they did. This instance is meant for level 35-45 and is much larger than it seems in the video. I skipped large sections of the instance as they aren't necessary for the achievement.
I'm rarely asked how to find the Stockades in Stormwind but for those of you who play exclusively on the Horde and may not know, here's a video showing how. This is much easier to get to than Ragefire Chasm in Orgrimmar (especially for Alliance players) but can be just as deadly and frustrating as you have to pass through the main area where players congregate in front of the Auction House and the Bank. Have fun!
For those of you who asked here is how to get to Ragefire Chasm in Orgrimmar. There are actually two ways of getting there: through the front door, or through the side door. I show both in the video but I would recommend using the side entrance. There are usually fewer players on that path so your chances of being killed are less, but there are more guards. As you can see in the video I died going in the front entrance. I didn't notice the DOTs on me quick enough to dispell them. If you're trying to do this at a lower level be prepared to die. A lot. I would suggest removing all of your gear so that when you finally reach the instance it isn't completely broken.