To get to the Special Stages in Sonic CD you have to get 50 rings and make it to the end of the level and jump into the giant ring at the end. Once there, you have to destroy all UFOs in the level before time runs out. Touching the water will make time drop drastically and when time gets low a new (blue) UFO will appear. It will make a sound when it appears and will stay in the middle of the level. When this UFO appears you need to destroy it to get more time. Destroying all the UFOs in the Special Stage will award you with a Time Stone. There are seven Time Stones in all and they can be gotten in all first and second acts in the game. In this version of the game the UFOs are properly scaled so you will be able to judge your jumps better than in the other versions of the game. This achievement will pop during the Special Stage score tally after you have gotten your seventh Time Stone.NOTE: If you do not get all 7 Time Stones in one playthrough you will have to start another playthrough and try again.
If you are having trouble in a Special Stage (like time running out and there is nothing you can do) just exit to the main menu from the Special Stage. Your save file will be on the same special stage when you get back to it so you can start it over.