A hatchet job is an unfair attack on someone, especially a written attack. A newspaper article disguised as a movie review might, on closer inspection, actually be a hatchet job on the film's director.
If you misrepresent or malign someone, particularly in a public way, that's a hatchet job. Writing a gossipy tell-all memoir about your family and close friends might feel like a hatchet job to them if you reveal their secrets and exaggerate their flaws. The phrase hatchet job comes from the earlier hatchet man, 1880s California slang for "hired Chinese assassin," from an earlier military term for the solider in front who cleared the way for troops.