1. Get a mushroom and save it. When a Blue Shell is coming, use it when the Blue Shell is about to hit you.

2. Go to a course that has a cannon (like Rainbow Road, DK Summit, Mayble Treeway). If a Blue Shell is coming to you and if you're near a cannon, stop wait for the Blue Shell to come. If it about to hit you go into the cannon and you should be fine.

3. This may be impossible to do. Go to Mayple Treeway, go to the place with the Wigglers and find a Star in a bush on the left side. Go to it and you're invincible; if a Blue Shell is coming and if you're in star mode, you're lucky.
P.S. Sometimes you find a Star on a different course if another racer drops it if they get hit by lightning or a bullet bill.