Joy Ride

Here's how to do this achievement:

1. 
   
2. Go to the tower at ~66, 20. You can use an elevator on the side of the tower to get up there.
3. 
   
4. Talk to Bilgewater Rocket-jockey next to the goblin selling Engineering Supplies
5. 
   
6. Pick the 4th choice: "Southern Rocketway Terminus, please."
7. 
   
8. Wait until the rocket has taken you to ~51, 75. Once you land, you'll get the achievement.
9. 
   

Or if you're at the southern side of Azshara, talk to Bilgewater Rocket-jockey and pick the 4th choice, "Northern Rocketway Terminus, please."
Note: I didn't get a chance to try it from south to north but since the achievement doesn't specify that you should go to either south or north, I'm assuming you get the achievement both ways.

Saw various comments down voted for saying this. Bit harsh. So allow me: Definitely Horde only. The NPCs you must talk to are hostile for Alliance players, despite there being a mix of friendly/hostile at the terminuses.

So impossible for Alliance toons. As per indications elsewhere on this webpage. But you came here before you knew that, just to be sure.

(Lol, getting down voted too! C'mon! Don't be gutless, say why you down voted. I don't bite!)

To elaborate, it only counts when you go from the very end to the "other" very end. To get this achievement, talk to a Bilgewater Rocket-jockey at the Northern Rocketway Terminus and take a ride to the Southern Rocketway Terminus, or vice-versa.