Dictionary.com
Thesaurus.com
Showing results for give it one's best shot. Search instead for give-it-one-s-best-shot .
Synonyms

give it one's best shot

Idioms  
  1. Make one's hardest or most enthusiastic attempt, as in I don't know if I can do it, but I'll give it my best shot. This expression employs shot in the sense of “attempt,” a usage dating from the mid-1700s.