The way you earn the Chaos Emeralds in Sonic The Hedgehog 2 has dramatically changed, as the Special Stage are different. You will also have more work to do as from this game onwards, there are 7 Chaos Emeralds to collect.
To enter a Special Stage, you must first collect a total of 50+ Rings. Then successfully complete find a checkpoint area in a level. It will then start spinning a circle of stars around the top of it. Jump into these stars and you'll be taken to the Special Stage.
In the Special Stage Sonic/Tails will be on a race course and you must successfully collect the required amount of rings the game asks you for. If you succeed, you'll do another lap with a new requirement of rings. Do this a total of 3 times, and you'll win the Chaos Emerald, and the achievement. If you fail you'll be eliminated and return to the checkpoint in the level you last touched.
The Rings in the arenas are usually scattered, as some make a trail, some go on the sides, some go close to enemies and some even are high up the top of the screen. So you'll need eyes all around especially the harder levels.
There are also Bombs which are in the arena as well. They are deadly as if you get hit, it will delay you from collecting anything for a short period of time and you will lose a few rings. So you must watch carefully where you move.
Tip: It is best to earn this achievement with one character. If you play with Sonic & Tails, the AI Tails is 100% useless as he'll only follow you, and will likely get knock out by the bombs or get lost.
Tip: When you get on the harder courses, each time you successfully pass a ring requirement... SAVE!! They get extremely harder and saving is the best way to succeed.
Note: The last level where you'll see checkpoint is on top of the Aircraft in the Wing Fortress Zone. There are no more checkpoints after this area.