Defeat the greatest! (4)
I believe the answer is:
best
I believe this is a double definition.
'defeat' is the first definition.
(besting is a kind of defeating)
'the greatest' is the second definition.
(thesaurus)
(Other definitions for best that I've seen before include "Of the highest quality" , "former football star" , "Overcome" , "The finest - worst" , "Superlative" .)