You need to choose Tails as your playable character in order to get this achievement. Start up the game and then choose any save data (you can also choose the No Save Data if you wish). Press

or

until you find a picture of Tails on his own. When you are ready press

to begin.
There are 2 acts in each world you visit in this game. Angel Island is the first world. You need to get a total of 100 Rings in any of the 2 levels and hold onto 100+ at one point during the game. Rings are the collectible items Sonic & Tails collect (similar towards the Coins in the Super Mario games). If you get hit by an enemy you will lose all of your rings. Power-Ups in this game protect you from an extra hit should you get hit by an enemy (e.g Water Bubble, Fire Shield, Lightening etc).
Whilst Tails is not as fast as Sonic, he has the ability to fly which can be done by pressing the jump button once and then holding down the jump button to fly for a short period of time (traditonally it's

). If Tails is in the air for too long he will get tired and you will glide down to a surface.
Like Sonic though, Tails can perform a Spin Dash by pressind

and then the jump button (

).
Use this to your advantage as you look for Rings. You do have to rush to complete the level, but you are on a 10 Minute Time Limit, and should you take too long, your character will lose a life and get placed back at the nearest checkpoint you obtained. In addition, should you complete Act 1 of the Angel Island Zone, Act 2 will start you off with 0 Rings. This, basically means Rings from the first Act, cannot be carried to the second act.
Once you have obtained 100 Rings or more, you will hear a chime sound earning you an extra life and the achievement will also unlock.
Tip: The boss that appears in Angel Island: Act 1 the first time is actually a cameo. He appears and then burns the island, giving you access to a further path in the game. He will be a boss however the 2nd time you meet him.Tip: You can get additional rings by playing the Bonus Stages in the game. You will need 50+ Rings and then when you hit a Checkpoint, you will see stars spinning on top of it. The bonus stage will have a huge slot machine in which you use Springs to open the slot and reveal a prize. Sometimes Rings will appear.Note: You cannot get additional rings in the Special Stages and the Rings in the Special Stage will not carry onto your total rings in game-play since they'll be converted to points as soon as you complete the Special Stage area.Here is a video to help you. Credit goes to
Gaming Unwired...
I hope you enjoy your short period of time playing this game.
Good luck!