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'.
(..) Someone has trifled with your brakes. The underworld will stop at nothing. This is the second attempt on my life. I may have caught my death of pneumon- Gesundheit. I have fixed your doorbell from the ringing. (..)1975 The Return of the Pink Panther