do/try your damnedest
do (one's) damnedest
To try one's hardest (to do something). Traffic out here is terrible, but we'll do our damnedest to get there on time. I'm doing my damnedest to get an A in this class, even though I'm terrible at math.
try (one's) damnedest
To put forth the maximum amount of energy or effort toward some task or goal. Money is a little tight at the moment, but I'll try my damndest to be there for your wedding.
do your damnedestINFORMAL, RUDE
If you do your damnedest to achieve something, you try as hard as you can to do it. I did my damnedest to persuade her. She was doing her damnedest to look as if she didn't care. Note: People sometimes use try instead of do. Ted tried his damnedest to explain things.
do (or try) your damnedestdo or try your utmost to do something.
The superlative form of the adjective damned is used here as a noun and can mean either ‘your worst’ or (more usually now) ‘your best’, depending on the context.