This university is highly renowned within the country.
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history
赫赫 comes from the 《诗经·小雅·节南山》: 「赫赫师尹,民具尔瞻」 — 'mighty Grand Tutor Yin, the people all look up to you.' 赫 doubles the character (赫赫) for intensity: 'blazingly, dazzlingly prominent.'
usage
Almost always precedes a noun via 的: 赫赫有名的人物/企业/家族. Slightly formal — a cut above the everyday 有名 or 很出名, implying real stature, not just popularity.