What is the ruling on taking revenge on those who slandered a person and damaged his reputation, and what is the appropriate revenge, and is retaliation in kind permissible?

If a person aggresses against another, the aggressed party is permitted to retaliate in kind, provided that the aggression pertains to human rights, such as جنايات (crimes/offenses) and الأموال (property), and that the retaliation does not lead to an infringement upon the rights of Allah or the commission of forbidden acts.

Your friend is not permitted to retaliate against those who wronged him concerning his honor and reputation by means of false statements and backbiting, because these are forbidden acts and major sins. It is not permissible to describe the oppressors as "scoundrels."

Supplicating against the oppressor is permissible for the wronged party if he does not wish to pardon them.