Here is the full list of all 13 Dino Eggs: Rebirth achievements.
Leap a flaming tar pit
Jump across two spider threads
Earn a bonus life
Warp out with 30 or more eggs
Warp out with 12 or more baby dinos
Save 3 babies of the same species at once
Find and save this rare baby in Outlands
Find and save this rare baby in Swamplands
Find and save this rare baby in Stone Age
Find and save this rare baby in Ice Age
Thwart Dino Mom with a boulder
Get eaten by Dino Mom
Reach the time warp just before devolution