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