Difficult objections raised and delivered (8)
I believe the answer is:
stubborn
'difficult' is the definition.
(difficult can mean stubborn or inflexible)
'objections raised and delivered' is the wordplay.
'objections' becomes 'buts' (as in 'no ifs, no buts').
'raised' says the letters should be written backwards (going up in a down clue).
'and' is a charade indicator (letters next to each other).
'delivered' becomes 'born' (as in a baby being delivered).
'buts' backwards is 'stub'.
'stub'+'born'='STUBBORN'
(Other definitions for stubborn that I've seen before include "Obstinate, unyielding" , "Tenaciously unwilling to give in" , "Obstinate, pig-headed" , "Unwilling to yield or grant a point" , "Determined" .)