It is said that the best way to handle an arrogant person is to understand why he or she is arrogant. Arrogant individuals seem to believe they are always right about everything and are better than most ordinary individuals. Arrogance is like a shield to cover an individual's insecurities because he is afraid of rejection and criticism. But, it is not hard to hit an arrogant guy's weak spot.
Treat him as if he is not the center of the world. Let him know that he is just like everyone else by not giving him as much attention that he is use to. You do not have to ignore him but just let him know that he can not get all of the attention he wants. Do not give him attention. If his arrogance is ignored, he will forget about being superior while dealing with you.
Prove the arrogant guy wrong about him being better at everything than others. Show him that you can do things of importance to him. This is his weak spot, but eventually, he will become impressed by you.
Show confidence in yourself and be sure not to become arrogant, like him. By then, he will give you attention and no longer show an arrogant attitude toward you.