It goes badly for bighead (6)
I believe the answer is:
egoist
'bighead' is the definition.
(I've seen this before)
'it goes badly' is the wordplay.
'badly' is an anagram indicator (letters in the wrong order).
'it'+'goes'='itgoes'
'itgoes' anagrammed gives 'EGOIST'.
'for' acts as a link.
(Other definitions for egoist that I've seen before include "Self-absorbed person" , "ill with him to think of others" , "A self-obsessed or very vain person" , "He puts himself first" , "number one fan" .)