To perform or behave in an exaggeratedly theatrical, flamboyant, or self-consciously artificial manner for comic or dramatic effect.
"The pantomime villain really camped it up, and the audience loved every minute of it."
He camped it up outrageously, winking at the camera and swishing his cape.
— Commonly used phrasing in British theater/film reviews; representative of widespread critical usage in publications such as The Guardian and The Times.