。
His poor education did not hinder his advancement.
Literal
Poor academic-record [subject-が] his advancement [possessive-の] hindrance [quotative-と] [topic-は] did-not-become.
貧しい学歴 means 'poor educational background.' 出世 means 'advancement, getting ahead in life.' 妨げとはならなかった means 'did not serve as an obstacle' — the は adds emphasis on the negation. A sentence about education not being destiny.