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
Collect all the Time Stones
Complete a zone in the Good Future
Collect 200 Rings
Get a hug from Amy
Travel through time
Pass the upper Signpost in Collision Chaos Zone 2
Find the angel statue in Wacky Workbench
Defeat Metal Sonic without getting hurt
Complete the Time Attack mode in under 25 minutes
Destroy all the robot teleporters and Metal Sonic holograms in the past