I think you fall well within the 'cute girl' category. You'll easily meet the manager's standards.
Literal
You [topic-は] sufficiently cute girl [possessive-の] category [to-に] enter [quotative-と] think. Manager [possessive-の] discerning-eye [to-に][topic-は] easily meet-[regret/completion-てしまう][probably-でしょう].
範疇 'category' is a somewhat formal word. おめがねにかなう 'to meet someone's discerning eye/standards' is an idiom — お眼鏡 (honorific for 'glasses/eye for quality') + かなう 'to match, to satisfy.' 余裕で 'easily, with room to spare.' The てしまう here conveys inevitability rather than regret — 'you'll end up meeting them whether you try or not.'