The pharaohs of Egypt were absolute rulers and dispensers of patronage. Thus a letter of admiration would have an overt purpose of praising and thanking the pharaoh for his wise and just rulership, It would have the covert aim of trying to gain appointment to a lucrative position or other types of favour.
Your first task as a writer is to choose the pharaoh to whom your are writing and look up his deeds. Then you should praise what he would have been lokely to have considered his major achievements. For example, for Akhenaten, one would praise his religious reforms, but one might praise Narmer for his unification of Egypt.