In the Spring Stadium Act 1, find the invincibility screen and break it open. While the music is still playing, quickly find the gold shield screen and break that open. The invincibility music will play the whole act. If it doesn't work, try again.
Requirements: 1) Make sure that you get all 7 Chaos Emeralds before you get to Mushroom Hill Zone. 2) If you've done step #1, when you get to Mushroom Hill Zone, Giant Ring's from now on will glow and when you enter them you'll be teleported to a room with the Master Emerald - step on the Emeralds here to do the Bonus Stages. 3) Now when you beat the Bonus Stage you'll get Super Emeralds - get all 7, collect 50 Rings and double jump to become Hyper!
Sonic 2 & Knuckles: Play Sonic the Hedgehog 2 and Sonic Spinball 20 times each. Sonic 3 & Knuckles: Play Sonic the Hedgehog 3 and Sonic & Knuckles 20 times each. Blue Sphere: Play Sonic the Hedgehog and Sonic 3D Blast 20 times each. Flicky: Play Dr Robotnik's Mean Bean Machine 30 times. Flicky (alternate): Have a Sonic Adventure 2 Battle Save File on your Memory Card. Ristar: Play Blue Sphere, Knuckles in Sonic 2, Sonic 3 and Knuckles and Flicky 30 times each.
Playing means opening the game - so, to do this quickly, as soon as you see the game's Title Screen, hit Z, return to the game menu and repeat!