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.
Find the angel statue in Wacky Workbench
Collect all the Time Stones
Collect 200 Rings
Pass the upper Signpost in Collision Chaos Zone 2
Complete the Time Attack mode in under 25 minutes
Defeat Metal Sonic without getting hurt
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
Complete a zone in the Good Future
Travel through time