Zygarde

If I have Florges with "Calming Aroma" in play my attacks cost one Fairy Energy less. So I think I can use Zygarde's "Core Enforcer" attack without a Fairy energy attached, but what about the part of the attack that says to discard one Dark and one Fairy energy from this Pokemon?

You do as much of the attack text as you can, which in your situation means simply discarding one Dark energy.

If I have a Dark Energy, a Rainbow Energy, and a non-Fairy energy card attached to Zygarde, when I use Zygarde's "Core Enforcer" attack can I discard the Rainbow Energy first for the Darkness discard, and then without a Fairy energy attached I'm done?

No, since you have Rainbow satisfying the Fairy Energy condition you would have to discard both the Rainbow and the Dark Energy.