You will first need to collect all 7 Chaos Emeralds in the game. Once done you will have the ability to transform into Super Sonic!
To transform into Super Sonic, simply collect and hold 50 rings then press and hold the jump button. You will be invulnerable and you will have extreme speed. This ability is limited though, as each second decreases your amount of rings. Once the rings have dropped to 0, you will lose your ability.
You will get this achievement as soon as you turn into Super Sonic.
Note that there is another achievement which requires you to become Super Sonic for a period of time...