difamar

To defame or libel — damage someone's reputation with false or malicious statements, spoken or written, and used in both everyday and legal Spanish: difamar a alguien en las redes sociales, una demanda por difamar.

• El periódico fue demandado por difamar al alcalde. — The newspaper was sued for defaming the mayor.
• No deberías difamar a alguien sin pruebas. — You shouldn't defame someone without proof.
• La campaña lo difamó públicamente durante las elecciones. — The campaign publicly defamed him during the elections.

Using difamar loosely for any criticism or insult — it specifically implies damaging someone's reputation with false or malicious claims, closer to the legal sense of 'defame/libel' than to ordinary criticar or insultar.