Epic is a type of Mission, it will appear evey few days on the Headquarters page once you have a certain number of recruits under your command. In an Epic Mission your main army is assisted by the best of your recruits, together you fight an assortment of non-playable troopers which usually outnumber yours by a notch and can carry more than 3 pieces of 
Equipment, but lack in levels after the first couple of 
Waves.
Despite the mission being larger in scale, a player is awarded the very same 4 
Credits for completing it as any other daily Mission.
Gallery
Mission background.
Full mission artwork.
Media
650px|Example of "Epic" missions.