aim high

aim high (third-person singular simple present aims high, present participle aiming high, simple past and past participle aimed high)

1. (figuratively) To set very ambitious goals for oneself.

   Near-synonyms: play big, think big

   • 1914, Journal of Experimental Pedagogy and Training College Record, page 314:

     In intellectual and moral matters we believe in having standards difficult of attainment, we cling even to standards which no one has ever yet attained; we prefer the person who aims high if only to fail: we definitely allow for the mishaps of the young and inexperienced and sympathetically help them to their feet.

• reach for the stars
• shoot for the moon

• “aim high”, in Merriam-Webster Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.