。
She boasts too much.
Literal
She [topic-は] boasting [subject-が] excessive.
自慢が過ぎる (boasting is excessive) uses 過ぎる (to exceed/be too much) as a predicate — her self-praise has gone past acceptable bounds. This is a blunt criticism: someone who brags so much that others find it grating. The construction [noun] + が過ぎる is a concise way to say 'too much [noun].'