The phrase "reach for the stars" is an idiom that means to set high goals, and to strive towards achieving those goals with determination and persistence. Some synonyms for this phrase include "aim high", "aspire to greatness", "pursue excellence", "strive for success", "dream big", "set your sights high", "shoot for the moon", "reach for the top", and "climb the ladder of success". All of these synonyms suggest that one should not settle for mediocrity, but rather should work hard to achieve their full potential and strive towards achieving their goals, no matter how difficult or daunting they may seem.