There are a variety of synonyms for the phrase "cast reproach upon" that convey a similar meaning. Some options include "discredit," "defame," "vilify," "slur," "slander," "denigrate," "besmirch," "impugn," and "tarnish." All of these words suggest the act of making negative or damaging statements about someone or something, often with the intention of damaging their reputation or credibility. It's important to choose the appropriate word depending on the specific context, as some may be considered stronger or more severe than others. However, they all convey the notion of casting negative judgment or criticism upon someone or something.