It has been several months since the attack of that cyclops and the phoenix. I'm researching about hybrid monsters. I've already gathered a great amount of army so I already did what Zieglind asked me to do. So I have all this free time to do my research.
So as to what I found, hybrid monsters cannot spawn normally. They are a crossbreed between two different monsters by either using a soul fusion or forcing the both of the two mediums to breed.
Soul Fusion is a type of method wherein the souls harvested or released from a living being gets fused with another soul. For the Phoenix that Precia got, it'll be Faye and that phoenix. I'm pretty sure that's a Soul Fusion since they aren't forced together. Faye can come out of the phoenix whenever she wants so there's that.
The force breeding method must've been the cyclops. But what did it get fused with? As far as I remember, cyclops doesn't have a regeneration ability.