Here is the full list of all 12 Sonic CD achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
Finish the game
Destroy Dr. Eggman's final machine
Destroy all the robot teleporters and Metal Sonic holograms in the past
Get a hug from Amy
Find the angel statue in Wacky Workbench
Complete a zone in the Good Future
Travel through time
Pass the upper Signpost in Collision Chaos Zone 2
Collect 200 Rings
Defeat Metal Sonic without getting hurt
Collect all the Time Stones
Complete the Time Attack mode in under 25 minutes