Original or Extra Crispy?

Achievement is rewarded in Ravenous Gorge.

Last boss chamber has three eggs that hatch and more birds appear when boss goes to mechanic ("Nimistrix cries out!"). Don't touch the egg and three more birds spawn. Birds spawn in order, first Starved, then Famished and last Rapacious.

Mechanic starts first time when boss goes to 75% HP. After that it repeats after 2-3 minutes. You have to wait and kite the boss if you want to kill all the birds. It also needs least 4 runs, since there are only 3 of each type of bird hatching on single run.

This is opposite to Eggscellent where you have to destroy eggs before they hatch.