。
She's full of herself about being beautiful.
Literal
She [topic-は] herself [subject-が] beautiful-person [is-だ] [quotative-と] is-being-conceited.
うぬぼれる writes in kanji as 自惚れる — literally 'to be infatuated with oneself' — a vivid compound that captures the meaning of 'be conceited, be vain.' The kanji form is uncommon outside dictionaries; in everyday use it's nearly always written in kana. The pattern [clause]+と+うぬぼれる embeds a self-flattering proposition as the content of the conceit — what she's full of herself about. 美人 (びじん) means 'beauty, beautiful person' and is gendered toward women in everyday usage; 美男 is the male counterpart but 美人 is far more common in conversation.