There are several synonyms for the phrase "hard-run". Some of these synonyms include "difficult exercise," "intense workout," "arduous run," or even "grueling jog". Essentially, any phrase or word that conveys the idea of running or jogging with a sense of challenge, difficulty, or struggle can be used interchangeably with "hard-run." Other possible options might include "challenging run," "tough jog," or "demanding exercise." No matter which synonym is chosen, all of them convey the same sense of physical exertion, struggle, and effort that comes with a challenging run or workout.