This is one of those things that isn't obvious: trying to just grabbing the eggs and fighting the biological horrors in Permadeath is going to get you killed . The trick is that you have to understand how biological horrors behave: they won't chase you indoors. This means that you can go to an abandoned building, build walls and roof around most of the eggs and put a door, leave one of the eggs outdoors. Now shoot one of the outdoor eggs, run like hell back indoors and you can harvest the indoor eggs at your leisure. I learned this trick from the following video from Scottish Rod , he has fantastic NMS content and is well worth a subscribe:
A blog about No Man's Sky.