A quick update as to what is known at this time:
According to an MMO-Champion thread (currently found here), the achievement has now been acquired by one raid group - Set Sail for Fail, EU-Lothar. The screenshots in said thread give an interesting indicator: The golden egg is being carried, and the carrier is one of the people with a 'flight' buff.
While the poster is being a touch coy, the hint they offer is "Watch the upper nest near the first nest."
Short Brainstorming Analysis:
Given the clues above: Odds are good the golden egg spawns near the start of the fight in this out-of-the-way location. Someone has to get the feather-flight buff, head up to the spawn location, and pick it up. Unknown at this point what all can break the egg.
Possibilities for causing egg-breakage:
The carrier dying. If this doesn't break it, the wording of the achievement combined with the egg being carry-able suggests it could be blown off the edge on its own if not being currently held. This would also explain why previous attempts to find the egg mid-fight failed - it fell and vanished after the first Downdraft.
The egg having its own lifebar to heal up, breaking when it reaches zero, a la Tsulong's tree achievement.
The carrier being blown off the edge while holding the egg.
The carrier taking too much damage in a single blow, requiring cooldowns on them during quills, perhaps (seems less likely, but I wouldn't put it past Blizzard).
The first two seem the most likely, to me. In any case, with this initial bit of guidance, hopefully multiple raid groups can give it a shot this week and report back on their findings. Also report on whether the egg spawns each pull or is a one-shot thing each week, if possible.
Found from http://www.wowhead.com/achievement=8097#comments.