Synonyms of bend over backwards in English:

try one's hardest, try as hard as one can, do one's best, do one's utmost, do all one can, give one's all, make every effort

strive, struggle, apply oneself, exert oneself, work hard, endeavour, try

do one's damnedest, go all out, pull out all the stops, bust a gut, move heaven and earth, give it one's best shot

NZ Australian go for the doctor