On the title screen (where Sonic the Hedgehog is visible), press UP, DOWN. LEFT, RIGHT, UP, (B), (B), UP, DOWN, LEFT, RIGHT, (X) + START to access the Level Select screen with Debug Mode enabled.
Select Special Stage and when it starts press (A) to turn into a Ring and proceed to the Chaos Emerald and press (A) again to collect it.
When the Green Hill Zone loads up, pause and press 'Start' and (X) together to reload the title screen.
At the title screen press 'Start' and (X) together to access the Level Select screen again and pick Special Stage. You will now be on the second Special Stage.
Repeat this process until all the Chaos Emeralds are yours and the achievement unlocks.