You just get an extra bonus if you you can kill one without using very strong otherworldly powers. For instance if I had a magic power to create black holes, I could just sink the monsters into one so it couldn't fight back, and for the purpose of this training mission that would be cheating.

I'll ask the Commander about your particular limit break, but would you be willing to give me a prior demonstration fighting against a T-Rexaur in the Training Center? From the sounds of it, it just enhances your GF and regular fighting strengths which is something spells here could do, so I don't think it'd be a problem.