Almost deserved a fight (4,5)
I believe the answer is:
just about
'almost' is the definition.
(synonyms)
'deserved a fight' is the wordplay.
'deserved' becomes 'just' (I've seen this before).
'fight' becomes 'bout' (synonyms).
'just'+'a'+'bout'='JUST ABOUT'
(Other definitions for just about that I've seen before include "More or less - at the point of starting" , "Barely" , "Almost exactly or completely" , "Almost exactly, informally" .)