You have to throw the bomb so that it detonates as it reaches Vaati. You can't just throw bombs all willy-nilly – they will be thrown out of the tornado and you'll find yourself getting hurt more than Vaati ever will.
Keep throwing bombs into the tornado, if you do it right it will get shorter. Quickly throw two more in so that the tornado is gone. This will stun him so slash away like crazy! Repeat until defeated (or at least it looks like he's defeated).
~ First Phase ~
When Vaati appears in that little jar thing, he starts a tornado below it causing him to fly up. Grab bombs from the pedestals and line up your characters on each cardinal point of Vaati. He should be on the square in the middle. Have one Link throw a bomb, and press "Y" for it to explode when it comes near him. Repeat this process until he gets to the floor. You can either shoot arrows at him from a distance or slash like crazy at his eye thing. Repeat all of this three times and you should beat his first phase.
~ Second Phase ~
His second phase is a little trickier. He comes out of his jar and now it's his true form. He will have two attacks this time. For the first one, he will make these spiked balls appear around him. He will float around trying to hit you with these. You can hit the balls back at him by just swinging you sword when he flies around. He will eventually stop and release all the balls in every direction. Hit one and it will change a different color and float toward a different color player. Switch to that player and hit the ball. It will go to a different player and change color (if you have more than two.) Repeat this bouncing back in forth and it will eventually go toward Vaati dealing him some damage. In his second attack, he has vines which he will show you the pattern of one (based on the color of your playes.) He will spin around in attempt to attack you. When he stops he will open the vines. Head toward the one with your color (while the other player goes twoard the other one) and slash like crazy. Repeat this and you should defeat Vaati for good.