do our damnedest拼死命干
do one's damnedest竭尽全力
try one's damnedest尽自己努力;尽自己最大的努力
PHRASE（习语） If you say that you will do your damnedest to achieve something, you mean that you will try as hard as you can to do it, even though you think that it will take a lot of effort. 全力以赴 [非正式，粗话][usu PHR to-inf]
I did my damnedest to persuade her.
我已经全力以赴地去说服她了。