There is a short bridge to a small entrance on the west side of Orgrimmar that goes over the Southfury River. There is a very small spot below the bridge that can be fished and counts for Orgrimmar. It is hard to get to the exact spot and may flag you PvP trying to find the spot, but few Horde players look down there.
For Horde, one way to do this in Stormwind without dying is to go to the right side of the entrance on the other side of the mountains blocking anyone from getting in by foot. Mind you this requires the ability to fly. Go to the right of the small stone building, cast your line and successfully hook a fish and then you gain the achievement, assuming you have gone to Orgrimmar already.
Patches and hotfixes
Patch 3.1.0 (14-Apr-2009): While phased for the Wrathgate quests, fishing in Orgrimmar now yields only trash, not fish. Hence, this achievement is not attainable while phased. If you are in the Alliance, A Low(1-10) to Medium Level (11-45), and are not in a pre-existing guild with Armor that is Binded to your account, there is a very high chance that you may die a few times before every reaching the inside of Orgrimmar, same thing applies with the Horde in Stormwind.