Sonic The Hedgehog 3

Extremely easy to get and can be done on any level if you look in the right places. You need to look for the giant golden rings, there is one within the first minute of the first level which is where you will more than likely get this achievement.

After the first encounter with Knuckles head to the right, after jumping over the rhino badnik and the spike traps drop down and then do a spin dash (Down + A) against the left wall, it should break and reveal a giant ring - simply jump into it.

You will be transported to a '3D' special stage full of red and blue sphere's, your aim is to collect all the blue spheres in order to get an emerald. Collecting a red sphere will cause you to leave the special stage empty handed so avoid these.

A trick is that if there is a square box of blue sphere's, collecting the outer ones will cause the inner ones to be automatically collected once you go around it. It will also turn them all into rings.

(You might want to check out the Points I and Points II achievements too as these can be unlocked along with this achievement)

(Check out the Complete Chaos Achievement for the first 7 Giant Ring locations)

Chaotic - 10G (Original Achievement)

Difficulty: 2/10

To get this Achievement, you must collect a Chaos Emerald.

In every zone there are Giant Rings that can be found. Jumping into said rings will send you to the Special Stage where you can play for a Chaos Emerald.

In the stage you will start running and you cannot stop, the goal is to run over and collect all of the Blue Spheres in the stage, and once all of them are collected you will receive a Chaos Emerald.

However, once a Blue Sphere has been collected, it will turn into a Red Sphere. If you touch a single Red Sphere, you will instantly fail and will be removed from the Special Stage.

You may also come across a Yellow Sphere in here, which causes you to jump forward a set distance which may be needed to get to other Blue Spheres, however they may land you in a pile of Red Spheres if you are not careful!

As time passes in a Special Stage, you will begin to speed up and the music will speed up to match. Beware this, as it has been known to be the cause of several fails.

Another thing to note, is that there are often "Grids" of Blue Spheres in 4x4 groups (such as this video) or a minimum of 3x3 groups. If you collect only the outside Blue Spheres in a grid, you will instantly collect all of the inside spheres as well as turn all the Red Spheres into Rings.

Lastly, if you collect all the Rings in a stage, you will get a Perfect, which in the 1st Special Stage alone, can net you over 40,000 points and get you the Points I and Points II Achievements at the same time as Chaotic once you collect the remaining Blue Spheres. (Refer to video)

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.

Sonic The Hedgehog 3 First Seven Special Stage Rings Locations

Just a quick video showing you where 7 special rings are

http://www.youtube.com/needtoachieve
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in addition to the other solutions, it is possible to save the game ANYTIME, so it is advisable to save before you start, but also, you can save during the special stage (just make sure you save in a place you dont mind resuming from). i always do this on a second save slot incase i save in a bad place and want to restart the level.