Hop on Genesis 2 to get the free tek armor from there.

Then travel to Aberration this suit works as a unbreakable hazmat armor and can be charged freely in the element water in the red zone (fully charge it you can See the percentage on the armor in your inventory).

Now you can just fly into the rock drake cavern while pressing sprint and controle grab an egg and just fly back out there you go you have your first egg.

More Rock Drake Taming & KO Tips