Load up Cairo Station on Legendary. Turn on Scarab, Envy, and most importantly Thunderstorm skull. Thunderstorm is the one that is actually required for the egg.
You must get to the bomb room without taking any damage whatsoever, but you can restart your last checkpoint if you do so it's not that bad. When you get to the bomb room, activate your cloak and hang a left around the corner. Head to the back of that room and wait for the egg to start and your achievement to unlock. There's no need to kill the Elites in the bomb room or wait in there with them.
This easter egg was much, much more difficult on OG Halo 2, unless you did the permanent cloak glitch, but even without that now the Scarab skull makes a world of difference.
I recommend a BR for precision aiming and to follow the path I take through the level in the video below.
I was actually one of the first 2 people to get this and had a video up yesterday, but I decided to remake the video to improve the overall quality and narration.