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.
例句
I did my damnedest to persuade her.我盡了最大的努力去說服她。
ADJ-SUPERL
令人萬分驚奇的;極為古怪的
If you say that something is the damnedest thing, you are emphasizing that it is surprising or odd.
例句
Today I heard somebody say the damnedest thing about Cross...今天我聽人說了關于克羅斯的最令人難以置信的話。You pick the damnedest places to eat!你可真會挑地方吃飯！