Castigate is a formal word that means "to criticize harshly."

// He was widely castigated for earning millions of dollars in bonuses as the company he was leading slid into insolvency.

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"At key moments throughout the animated feature, which takes her from age 7 through her 20s, she’s bombarded with the song stylings of three Mythology Sirens, harmonizing scolds who take different forms, depending on the circumstances. They reinforce Zelma’s self-doubt and castigate her whenever she breaks or questions the old-school rules of the boy-girl game …" — Sheri Linden, The Hollywood Reporter, 11 Oct. 2023

Castigate has a synonym in chastise: both verbs mean "to punish or to censure (someone)." They both also happen to come from the same Latin root, the verb castīgāre, meaning "to discipline for a fault or lapse; reprove, censure." Castīgāre is also the source of chasten, which can also mean "to discipline by punishment" but more commonly means "to subdue or make humble," as in "chastened by my foolish error." Castigate is the newest of the three verbs; current evidence dates it to the early 17th century, while chasten dates to the early 16th century, and chastise has been found in use as far back as the 14th.