bend over backwards
• make every effort to achieve something, especially to be fair or helpful.
• "we have bent over backwards to ensure a fair trial for the defendants"
Similar:
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,
go for the doctor,