Heroic: Garrosh Hellscream Guild Run

As of Patch 6.0.2 this is earned by doing mythic Siege of Orgrimmar, what is also know as former Heroic prior to patch 6.0.2.

This might change after i have made this comment, that is if they change the name of the achievement or difficulty in which you have to do this achievement on
(I doubt that they will change the difficulty you have to do this on)

Confirmed, you need to do Mythic, as of patch 6.0.2, instead of HC - confusing because the achievement still says heroic.

I can confirm that mythic is required. This is the message that I received from a game master in response to the ticket that I submitted:

I am Game Master ****, and after picking up your ticket I was more than happy to take the time to look into this for you.

Because of the changes to raid difficulties that happened starting with Patch 6.0, this achievement must be completed in the Mythic version, not Heroic. This is something that is due to be updated for a few of the achievements that state Heroic Siege, but actually require Mythic, since when the achievements came in, Heroic was the highest difficulty, whereas it was renamed Mythic under the new raid system.

Hopefully this hasn't slowed you down too much, and I wish you the very best of luck on your adventures through Draenor!