。
She brags about her beauty.
Literal
She [topic-は] her own beauty boasts.
Note the missing を between 美しさ and 自慢する: the standard form would be 自分の美しさを自慢する. Casual or compressed Japanese sometimes drops を, especially before する compounds — common in headlines, conversational speech, or when the noun + する pair is felt as a single unit. 美しさ ('beauty') is the productive nominalization of the i-adjective 美しい via the ~さ suffix (which converts adjectives into nouns denoting the abstract quality).