Really anyone can beat Nest, but there is a secret to attacking her. Attack her every round with a big hit once and then ignore her until she moves again. One attack, ignore. You have to start early in the battle. After she goes 3-5 times, she will die. People get in trouble by leaving her until last. You have to peck away at her over whole battle. Then she is pretty easy.
And I didnt see mentioned: Embo's kick can kill her in one hit at full health, but that requires his contract and is risky by waiting so long.