The cyclops smashes a man to the ground and eats part of his body (shown offscreen, however the result of it is shown and there is blood).
The Greeks attacked the Trojans, some brief violence is seen, and brief blood is shown
Odysseus and his men stab the cyclops in the eye with a stick (blood is shown)
Odysseus and his men are attacked by a monster in a cave (this is the most bloodiest part of the movie, blood is seen being sprayed on the walls after they are attacked.)
Men fist fight, there is some blood.
Towards the end, Odysseus and his son kill all the men that tried to steal his wife and his kingdom (blood is shown)