taru-adjective, adverb taking the 'to' particle
Literary, somewhat archaic adverb describing steady, painstaking effort. Often used in the form 孜々として.
彼は孜々として研究に励んだ。
He devoted himself assiduously to his research.
孜々として働く姿は周囲の尊敬を集めた。
His diligent work earned the respect of those around him.
勤勉 is a standard noun/adjective meaning 'diligent' or 'hardworking', used in modern speech and writing, whereas 孜々 is an archaic, formal adverb.
The exact derivation is uncertain; the kanji 孜 means 'industrious' or 'diligent', and the repetition emphasizes sustained effort. The word is a literary borrowing from classical Chinese.