The most common and most likely answer to this crossword clue is the 6 plus 2 plus 6 letter word CLUTCH AT STRAWS
I've seen this crossword clue in The Daily Telegraph
C
L
U
T
C
H
A
T
S
T
R
A
W
S
More clues leading to the result CLUTCH AT STRAWS
Buddy explains!

The straight part
We know that "Make a desperate attempt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make a desperate attempt = clutch at straws.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.