The phrase "injure one's reputation" refers to an action that causes harm or damage to one's standing or image in the eyes of others. Some synonyms for this phrase include "defame," "tarnish," "slander," and "smear." These words all convey the idea of an attack or assault on someone's reputation or character. Other synonyms could include "discredit," "degrade," "besmirch," and "vilify." It is important to remember the impact that injuring one's reputation can have on a person or organization, and to choose our words and actions carefully to avoid causing unnecessary harm.