You can make the eyes move on the horizontal axis based on the input of the player, but in a reduced speed ofcourse.
I don’t know how you initiate the boss fight, but once you start in have the boss look at the player.
For instance, I start my boss fight with a trigger, and when the player triggers it stuff happen. So you can set a “startingPoint” for your eyes, and then have them move left and right as I said before.
check the angle between the middle of the eyes of the cat and the player. Then choose a max distance the eyes can move to the side and max angle that your character can be for the cat to move his eyes. Then if looking directly down is 0Âş angle the eyes position will be -
eyeleft.transform.position = new vector3( angle * (maxDistance/maxAngle), 0,0);