What kind of functionality do you want for the boss? I can assume you are trying to make the boss face and follow the player but not sure if that's what you are trying to do. I've been able to set up this kind of functionality when the boss is a bullet or using 8-direction and have no issue with animation direction.
Again, it depends on what exactly you want to happen. You could have the boss switch animations based on if it does or does not have line of sight of the player if that's what you're trying to do, if it's specific areas on screen you could detect if player is overlapping a specific checkpoint, is a certain distance away from the boss etc, if you are switching the boss' animation based on stages of the boss then you could set up a variable for what stage of the fight it's at and switch the animations that way if for instance it's a boss that is being damaged and you want to change how badly damaged it looks.