Reproach means to mildly criticize. If you show poor manners at your grandmother's dinner table, she will reproach you.
The verb reproach means to express disapproval or criticism of; as a noun it means blame or criticism. If you are beyond reproach that means no one could find anything to criticize about you. Synonyms for reproach are the verbs admonish, reprove, rebuke, reprimand. As a noun, reproach can also be shame. If you are caught lying, it is a reproach that might bother you for a while.