。
She does nothing but suck up to her teacher.
Literal
She [topic-は] teacher [to-に] flattering [nothing but-ばかり].
こびる (媚びる) means 'to flatter,' 'to fawn,' or 'to curry favor' — it carries a negative connotation of insincere ingratiation. ~てばかり means 'does nothing but,' expressing that flattery is all she does, with implicit disapproval. The sentence ends without an explicit predicate — the いる that would normally follow (こびてばかりいる) is dropped, a common ellipsis in casual speech where the meaning is clear without it.