When it comes to expressing the idea of wasting one's efforts on something futile or pointless, there are various synonyms for the phrase "beating the air." For instance, one might say that someone is "spinning their wheels," "chasing their tail," or "barking up the wrong tree." Other possible expressions include "going nowhere fast," "wasting their breath," or "running in circles." Ultimately, all of these phrases share a common theme: they imply a sense of frustration and futility, suggesting that one's efforts are not leading to any significant progress or improvement.