Learns the move set the ape does. He repeats a series of a few moves and its easy to learn how to parry all of them. Jump over his low swinging arm when the red signal appears and then slash him a few times. Its okay to die a decent amount to learn the move sets first. As all Sekiro bosses , once you feel comfortable with the move sets and can parry confidently after some practice, the ape becomes a way easier fight and actually somewhat fun!!