Attack Pattern: He attacks whether or not you're facing him, and becomes invisible (and invicible) for a short period of time after each hit against him.
Basic Fighting Strategies: You have to hit him with three blue blocks. This shouldn't be too hard, as there are lots of them, but be careful about getting cornered. Try to keep moving around the room.
Advanced Strategies: One thing that took me a while to figure out at first is that you can kick blocks straight up by holding up and letting go of the Y button. This works much better than trying to jump and kick blocks at him.
Also, I recomend standing in one of the corners of the room when Bigger is invisible, and facing in, then running to the other end as you attack him, and turning around to face in again. This pattern should help to keep you from getting cornered.

Attack Pattern: He will try to follow you around when you're not facing him. If you do face him, he will fade out and stay still. You can't hurt him in this state.
Basic Fighting Strategies: Basically, you have to hit him using ricochets. Face away, aim an egg at the wall, and it should bounce back and hit him (if you aim properly.) I think he shrinks as he gets hit, which makes aiming harder.
Advanced Strategies: I don't know of any. Players who know this game are welcome to help me out here!

Attack Pattern: As usual, he follows you until you turn around, then he becomes invisible and invincible.
Basic Fighting Strategies: In the areas where the floor doesn't move, I recommend getting away from Boo, then crouching. As he gets close, do a backflip, and go into a "Pound the Ground" - or butt-stomp, as I like to call it. You don't have to backflip necessarily, but I find it helps a bit, because you're more likely to get right on top of him.
Advanced Strategies: In the carousel, just walk away from Boo (go in the direction opposite of the spinning floor, or you'll probably hit the flame-throwers.) Then stop, with your back to him, and do a butt-stomp as the carousel carries you back towards him. You might want to do a back-flip too.
It's also interesting to note that Mario can do regular stomps on Boos without taking damage in this game. Not particularly useful, but it might come in handy now and again.