Furiously rejected female killer? Not half! (4,3)
I believe the answer is:
like mad
'furiously' is the definition.
('like mad' can mean furiously or intensely)
'rejected female killer? not half' is the wordplay.
'rejected' is a reversal indicator.
'female' becomes 'dame' (dame is a kind of female).
'not half' suggests halving the letters.
'killer' cut in half is 'kil'.
'dame'+'kil'='damekil'
'damekil' reversed gives 'LIKE MAD'.
(Other definitions for like mad that I've seen before include "Furiously" , "Very quickly" , "wildly" , "With great intensity, energy, or enthusiasm" , "Energetically" .)