This sentence sounds a bit odd to me; however I believe it's grammatically correct. Could you please corroborate for me. Sentence: "She has been slandering me/her/him"
"To slander" is the verb. As a transitive verb, it takes an object (in this case, "me"). "has been slandering" is the correct formation of the present perfect progressive tense for the third person ("she").
So: Yes, it is correct.