Like One's Life Depended On It Meaning

(idiomatic) desperately

Example: 2011 January 5, Jonathan Stevenson, “Arsenal 0 - 0 Man City”[1], BBC:
  With Carlos Tevez chasing down every lost cause like his life depended on it, City always had an out ball but Arsenal had such a monopoly on possession that they barely had to give thought even to the Argentine.