It is very possible to skip every phase of Henterprise even at max difficulty as almost every weapons do relatively massive dps to bosses. The 3 major bosses are screen wide, so almost every damage dealt to them. To prevent 100% damage output taken, they have their own strategy, Yolk Star with its laser cannons, Egg Cannon with chicken wobble and egg launch, and Henterprise is supposed to be with its chicken and feathers.
But the problem is Henterprise didn’t come with it at the beginning. During shooting the big laser which in fact is too slow, it had no protection. You have 100% damage output, in this way, you can skip its all phases.
To prevent skipping Henterprise fight I have a simple solution: make its laser shooting period shorter. So it will start spewing feathers earlier to block your damage output.