break one's back vs give something a shot

break one's back

verb
  • Synonym of strive: to apply oneself completely to the point of physical exhaustion or incapacity. 

  • Used other than figuratively or idiomatically: see break, back. 

give something a shot

verb
  • Try or attempt (something); to give something a try. 

How often have the words break one's back and give something a shot occurred in a corpus of books? (source: Google Ngram Viewer )