Here is the full list of all 12 Sonic The Hedgehog (Arcade) achievements worth 200 gamerscore.
You beat Green Hill Zone Act 1 in under 35 seconds.
You got one Chaos Emerald.
You got 100 or more rings.
You cleared the Green Hill Zone.
Beat Marble Zone Act 1 in under 80 seconds.
Get to the Star Light Zone.
Get to the Spring Yard Zone.
Get to the Labyrinth Zone.
Get all the Chaos Emeralds.
Beat the game.
Beat the game in under 40 minutes.
Beat the game without dying.