To beat one’s victim is a bit fishy (7)
I believe the answer is:
lamprey
'a bit fishy' is the definition.
I can't tell whether this defines the answer.
'to beat one's victim' is the wordplay.
'to beat one' becomes 'lam' (I can't justify this - if you can you should believe this answer much more).
'victim' becomes 'prey' (prey is a kind of victim).
'lam'+'prey'='LAMPREY'
'is' acts as a link.
Can you help me to learn more?
(Other definitions for lamprey that I've seen before include "Freshwater eel-like fish" , "Eel-like animal" , "Marine carnivore" , "Fish-like vertebrate" , "seafood" .)