This is pretty much story related. During mission 6 of the story, you will be tasked with building an aviary and research Pteranodons. Build the aviary and select it with the A button. Press RB to go to the 2nd tab and change the number of slots to 6. You can then slap on a few success rate 2.0 mods and hatch 6 pteranodons. The quest will complete while the last one is being released, and the achievement will pop soon after.