Become less believable with victory involving something dirty (4,4)
I believe the answer is:
wear thin
'become less believable' is the definition.
(to wear thin can mean to become less convincing)
'victory involving something dirty' is the wordplay.
'victory' becomes 'win' (I've seen this before).
'involving' indicates putting letters inside.
'something dirty' becomes 'earth'.
'win' placed around 'earth' is 'WEAR THIN'.
'with' is the link.
(Other definitions for wear thin that I've seen before include "start to be ineffective" , "Deteriorate" , "Gradually dwindle" , "Diminish - become less tolerable" , "Become less convincing through overuse" .)