The achievement is completely system generated and from what I know about the eggs-tra achievement is that it can be obtained once you found the hidden eggs from the multiplayer map packs and not from Mayday. Here's a video I found for how they got it for Xbox One. But it's not an official walkthrough from Activision: Call of Duty: Ghosts - Egg-stra Devastation! Achievement Guide - YouTube
A support case was created for you and you should be contacted shortly by a Customer Support Representative, if you haven't been already. You can view and update your case at the Activision Support website. After logging in, go to "My Support" then "My Cases".