WoWDB

Note: This achievement was removed as a criterion of  Brewmaster in Patch 3.3.0.

Formerly named "Drunken Stupor" with the tooltip "Fall 65 yards without dying while completely smashed during the Brewfest Holiday." I presume it was changed in Mists of Pandaria around the same time as European game ratings board brouhaha over the brewmaster Monk's "Drunken Haze" and "Mastery: Drunken Brawler." /facepalm

There are a few good locations to attempt to earn this achievement, though the following list is by no means exhaustive. Also, make certain you have your  Synthebrew Goggles equipped.

Screenshots have been uploaded for each of these listed locations. I'm sorry about the one for Gates of Stormwind; an apple tree kept getting in the way so I had to use an angle that kind of distorts the perspective.

• Scryer Tier (Shattrath, Outland). Ride the elevator up to the top, then jump off of it before it begins traveling down. If you are not on good terms with The Scryers, then get on a flying mount and position yourself just above where the elevator stops. Dismount.
  
  
• Krasus Landing (Dalaran, Northrend). There is a parapet just outside the Landing. Get on a flying mount (your character needs to have trained  Cold Weather Flying) and position yourself level with where the fancy gold scroll-work begins on the purple top-stone. Dismount.
  
  
• Elevator (Orgrimmar, Kalimdor). Ride up the elevator closest to the Orgrimmar flight master and step off. Wait for the elevator to reach the bottom, then jump. Easiest Horde method in my opinion. 
  
  
• Gates of Orgrimmar (Orgrimmar, Kalimdor). Position yourself between the spikes that extend out into Durotar (zoom) and run straight off. You'll have to use a flying mount (and have  Flight Master's License) or have another player give you a lift. Fall damage from the west gate tower took my health down to under 5%; players, if you don't already have  Ultimate Triage, here's your opportunity.
  
  
• Gates of Stormwind (Stormwind, Elwynn Forest). Position yourself on the top-most riser which overlooks the cheese shop near the main entrance. Face your character west so that it is pointed between the two lower rises (one on the left, the other on the right) and run straight off. You'll have to use a flying mount (and have  Flight Master's License) or have another player give you a lift.
  
  
• Stormwind Docks (Stormwind, Elwynn Forest). Travel to the north-west large stone building which looks at the docks in Stormwind Harbor. Stand on the middle-level on the stonework with the middle riser firmly on your right side. Point your character directly forward and run straight off. You'll have to use a flying mount (and have  Flight Master's License) or have another player give you a lift.

Mages and Paladins can cheese this achievement by using  Ice Block and  Divine Shield, respectively. The game only checks for speed modifiers and distance fallen.