Story of boxer swinging both ways (5)
I believe the answer is:
alibi
'story' is the definition.
(story given by a suspect in an investigation)
'boxer swinging both ways' is the wordplay.
'boxer' becomes 'Ali' (Muhammad Ali).
'swinging both ways' becomes 'bi' (short for bisexual).
'ali'+'bi'='ALIBI'
'of' acts as a link.
(Other definitions for alibi that I've seen before include "Sort of explanation" , "Legal defence proving innocence" , "can offer a valid defence against most charges" , "Cover story" , "Excuse, defence" .)