A desperate attempt is a last-ditch effort made by someone who is in a difficult or hopeless situation and is willing to try anything, no matter how unlikely it may be, to escape their predicament. It's an action taken when all other options have been exhausted and there seems to be little chance of success. The phrase can also imply that the attempt made is not well thought out or carefully planned, but rather a frantic and impulsive reaction to the situation at hand.