This achievement is for completing the campaign on the difficulty setting "Hard". This is a pretty decent middleman between easy and inferno, and should definitely be done after completing normal. The reason for this is EDF isn't like most shooters where you can start off on hard difficulties off the bat, you need to complete them in order to build up your character of choice/get better weapons so you can handle the insects you are facing.
This is of course, unless you decide to play with your friends who just so happen to be quite a bit higher leveled and can run you through the stages, your choice. Though the first one tends to help more as if you are going for completion, you will need to rank up not only your main character but the other 3 classes as well. Online co-op is suggested but be warned, the game does get tougher the more people you have in your game and communication helps greatly.
These stages don't have to be done in any specific order and you can find a custom match for each stage on whichever difficulty if you need to knock a few odd ones out. The medals in the picture will show you which difficulties you have completed, going from right to left in difficulty (left being the easiest) and will give you an idea of what you have left to complete.