Succeeded cracking puzzles needing brains and hard fight (5,6,4)
I believe the answer is:
cross swords with
'hard fight' is the definition.
'cross swords with' can be an answer for 'fight' (to cross swords with someone is to fight them). I am not certain of the 'hard' bit.
'succeeded cracking puzzles needing brains' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'cracking' indicates putting letters inside (inserted letters go into a gap or crack).
'puzzles' becomes 'crosswords' (crossword is a type of puzzle).
'needing brains' becomes 'with' (I am not sure about this - if you are sure you should believe this answer much more).
's' placed into 'crosswords' is 'crossswords'.
'crossswords'+'with'='CROSS SWORDS WITH'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for cross swords with that I've seen before include "challenge" , "Struggle against" .)