Greek character breaks petty Cretan cross (8)
I believe the answer is:
minotaur
'cretan cross' is the definition.
(mythical hybrid of Crete)
'greek character breaks petty' is the wordplay.
'greek character' becomes 'tau' (letter from the Greek alphabet).
'breaks' is an insertion indicator.
'petty' becomes 'minor'.
'tau' placed into 'minor' is 'MINOTAUR'.
(Other definitions for minotaur that I've seen before include "Creature, half-man and half-bull, slain by Theseus in the Cretan maze" , "Monster in a maze with the head of a bull and the body of a man" , "Am in rout of a fabulous monster" , "Mythical man-bull" , "Mythical beast of Crete" .)