Instructions
Keep any mushrooms you gain if you are approaching first place. Use the mushroom right at the point that the blue shell rests above your head.
Use any boosts or jumps that are in range when the blue shell stops above your kart. Activate Star Power if you happen to be holding it to be protected from the blue shell's power. Take damage from a banana or a fake item box right before the blue shell gets to you.
Drive into a cannon on the Maple Treeway and DK Mountain levels to get away from a blue shell. Take the ramp over the river in DK's Jungle Parkway to escape the blast. Use the tunnel with the large stars on both ends in Rainbow Road to avoid it on that level.