Here are the cheats!
1st Egg - Gushing Geyser - Answer : Triceratops
2nd Egg - Mochlodon Theater - Answer : Catastrophists
3rd Egg - Prairie Pool - Answer : Pleistocene
4th Egg - Rumble Rocks Cave which is at Prairie Pool - Answer : Troodon
5th Egg - Carnivorous Cavern - Answer : Middle Jurassic
6th Egg - Secret Temple which is at Dino Dunes - Answer : Paleogene
And the reward...