make a pass at

Flirt or make advances to someone, especially of a sexual nature, as in “Men seldom make passes at girls who wear glasses” (Dorothy Parker, Not So Deep As A Well, 1936). [1920s]

Also, take a pass at. Make an attempt, as in I've made a pass at opening it but had no luck, or Jake, will you take a pass at changing the oil? This usage employs pass in the sense of a “jab” or “poke.” [Colloquial; 1900s] Also see make a stab at.