Once again, the way to earn the 7 Chaos Emeralds is much more different compared to Sonic The Hedgehog 1 & Sonic The Hedgehog 2. To earn them you've got to do some searching first.
Throughout all the levels you play, there are secret areas which contain Giant Rings which spin round in circles (like Sonic The Hedgehog 1 did). Find a ring and jump inside it to begin a Chaos Emerald Mini-Game.
You will then be placed in a 3D View, and your goal will be to run around the arena and grab the Blue Spheres, whilst avoiding the red ones. Touching the red ones will eliminate you and will return you to the level you are playing in.
Each time you touch a Blue Sphere, it will turn from blue to red. Successfully grab all of the blue spheres, and you will win a Chaos Emerald and the achievement.
You can earn rings in a special stage zone by finding a collection spheres of more than 4 and then running around the outer blue spheres, blocking the inside ones making a red sphere square.
Once you've turned the last sphere in the square to red, all the spheres in that particular location will turn into rings, which will give you extra points. The rings obtained in a special stage zone will not transfer to the level you are playing in. They will be used as points.
Additionally if you successfully grab all the rings in a Special Stage Zone that are available, you will be awarded "Perfect" which will give you 50,000 Points, which is an extra life in the main game.
Note: Be careful if your trying to turn the spheres into rings. If you go too far inside the square, or go off-course you may lead yourself to an area full of red spheres, and a trap.
Note: You can jump in a Special Stage as well by pressing the Jump Button. You will need to use this move when you do the harder challenges.
Note: The longer you last in the arena, and the more spheres you grab, the faster the music and the arena goes, so you need to watch yourself when the speed increases.