The image above shows you what the egg looks like, on your minimap it will appear as a yellow egg. The best strategy when doing this event is to just focus on finding the chests which will have randomly spawned somewhere on the map. There will be either 2 or 3 chests and while looking for them you should come across the egg nest anyway. Trying to determine whether there are 2 or 3 chests on the map can be tricky, if you have found 2 chests continue searching for a few minutes more so you are confident you have found all the chests on the map or until you find the egg.