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