09/17/15 - UPDATE!!!!!
achievement finally obtainable after a 4 month glitch was fixed with the new elemental evil update. Many dungeons were removed from the game and only 4 are left! Gear score was removed in favor of item level and now the minimum level to start an epic is level 70. A few new hurdles to jump through but the achievement IS obtainable once again!
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Epic dungeons are only available once you hit level 70. Epic dungeons also count towards the normal dungeon count for the "Dungeoneering" achievement (complete 10 normal dungeons)
Once you hit level 70, hit the menu button and go to quests. Under queues, you will see a list of the 4 epic dungeons you can select. These are identified by a new symbol. Normal dungeons have a gate door symbol, epics have the same symbol with what appears to be a dragon's head and wings above the door.
In addition to hitting level 70, you also must have the correct item level to enter each dungeon. If you hit menu and go to character sheet, under your level you will see your total item level. This is the total sum of the levels of all your equiped items. If you meet the minimum level, you can select to join a queue for these epics. Just do any 25 you like, you can do the easiest one 25 times if you wish. The following item levels are required for each mission
Lair of Lostmauth - 1,600
Cragmire Crypts - 2,000
Gray Wolf Den - 2,000
Temple of the Spider - 2,000