。
She takes great pride in her appearance.
Literal
She [topic-は] her own appearance [object-を] very-much pride [as-に] is-doing.
自慢にする (literally 'to make X into one's pride') is a slightly more grammatically transparent variant of 自慢する. The pattern X を Y にする means 'treat X as Y / make X into Y,' so 自慢にしている emphasizes the act of holding her appearance up as a source of pride. 容姿 ('appearance, figure') covers a person's visible looks more broadly than 顔 (face) — face plus body and overall presentation. 大変 functions as an intensifying adverb here ('very, greatly').