There are many synonyms for the phrase "make an attempt." Some of the commonly used synonyms include "try," "endeavor," "seek," "strive," "make an effort," "aim," "undertake," "venture," "take a shot at," "assay," and "have a go." Each of these synonyms conveys the idea of trying to accomplish something, but they may have slightly different shades of meaning. For example, "venture" suggests a risk or danger, while "assay" implies a more scientific approach to problem-solving. It is always helpful to have a variety of words at your disposal to express yourself more precisely and elevate your writing or speech.