Crush notes on achievement (6)
I believe the answer is:
defeat
'crush' is the definition.
(I know that crush is a more specific form of the action defeat)
'notes on achievement' is the wordplay.
'notes' becomes 'de' (two musical notes).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'achievement' becomes 'feat' (feat is a kind of achievement).
'de'+'feat'='DEFEAT'
(Other definitions for defeat that I've seen before include "Vanquish, win against" , "Beat, win against" , "Opposite of victory" , "Rout" , "Win over, frustrate" .)