You Can't Make a Giant Omelette...

The [object=235826] has a five (5) minute respawn timer and can be found on the highest peak on Darktide Roost at 61.26, 88.77. As others have mentioned, you can use [item=115020] found by goblins on the isle to get up there, or make clever use of items such as [item=119093], Goblin Glider Kit, or similar.

You have to be on the Garrison daily quest Assault on Darktide Roost to be able to interact with the eggs on the island. If the daily quest isn't available, you can buy a [item=122418] (A) from your Garrison Quartermaster for [currency=824 amount=200].

You can get a [item=115020] from the goblins on the isle. it makes it possible to climb the mountain in the middle of the island. the egg is on the top.

Can confirm 16th November 2014, this achievement is bugged (as is 'entering' the unmanned rylakinator - you can't interact with the vehicle). Made it to the top of the hill - the very highest point using the goblin pack and cannot interact with the egg.

EDIT: Looks like it's bugged for some people. Another person in my party went up to the top and got the achievement.

It's also brought to my attention that you may have to be on the quest Assault on Darktide Roost to be able to interact with the egg.

You have to be on the quest Assault on Darktide Roost to interact with all the eggs on the island.