Yup, the answer is Chrysalis Burst.
The first of simple make,
A second nearly raw,
This one was a bit of a stretch, but raw meat can also be called rare. Rare Egg.
The third of great majesty,
A fourth to be written of,
Legends and myths are written down, as stories. Legendary Egg.
Probably should have included something more, since it was pretty vague.