The Designate at her best is supposed to be some kind of cosmic force that elevates mortals across the Universe to the next level of evolution, into Gods or some such. At that level, she should beat almost anything.
They went back and forth then he used freeze breath to momentarily disable her IIRC.
But that was in her Thor Girl form, at that time she was a high end mid Herald in that body (Competitive but she'd lose to a true High Herald eventually). I assumed for this thread she could enter her Designate form and use her powers at her best or whatever.