Fear may be the mind-killer, but it’s a very necessary component of any character. For an action hero or any protagonist who deals with power (physical, psychological, spiritual, supernatural) how they approach fear will be the deciding factor in whether or not they will fall into the category of a bully.
For any true combatant (who isn’t a psychopath) overcoming the instinctual fear of harming themselves and causing harm to someone else is a key part of their training. How they handle the prospect and reality of causing harm to another, especially if that person falls into the category of “us” as opposed to “them”, will be a defining part of who they are. Combat is a terrifying, brutal, and uncomfortable place that is as much based in psychological willpower as it is a physical action.
Remember, fear is much more important than anger. Does your character face their fears? Do they run from them? Or do they inflict their fears on others?