What is the ruling on insulting the unjust, tyrannical ruler and supplicating against him?

It is permissible to supplicate against an oppressor and against a profligate who openly declares his wickedness. There are indeed sacred texts indicating the permissibility of this, including the supplication of the Prophet, peace and blessings be upon him, against oppressors, and the supplications of the prophets and companions against those who wronged them. Moreover, reviling a profligate for what is in him is permissible according to the majority of scholars, if the intention is to advise or warn, not to backbite.