It was a successful 'attempt at' climbing Mount Everest. = It was a successful 'attempt on' Mount Everest.
In an 'attempt' [='effort'] to raise money, the school will begin charging admission to school concerts.
She failed her driving test on the first 'attempt' but she succeeded on her second 'attempt'.
(..) that earlier this evening... Harry Potter was sighted in Hogsmeade. Now... should anyone... student or staff attempt to aid Mr. Potter? They will be punished in a manner consistent with the severity of their transcription, further more... Any person found to have knowledge of these events... (..)2011 Harry Potter and the Deathly Hallows: Part 2