Frozen Factory: Zone 2
Red Star Ring 1: Near the beginning of the level, you'll be shot through several billiards-themed areas. Knock all nine balls into their holes to unlock the Red Star Ring at the end of the sequence. Note that throughout this level, all collected rings will stick to Sonic's snowball form until you reach the nearest checkpoint.
Red Star Ring 2: Almost immediately after the pool table, you'll find the second Red Star Ring hanging over a square-shaped hole.
Red Star Ring 3: The third is clearly visible on the right side of a small area where you encounter one of the first crabs.
Red Star Ring 4: When you come to a large fork with a monster on the right side, take that path, knock the monster over the edge, and jump over a couple of platforms to reach the fourth Red Star Ring.
Red Star Ring 5: When you hit the second billiards-themed area, knock all of the balls into their holes once again. It requires much more maneuvering this time, and be warned that you'll forcibly hit a checkpoint at the end of the sequence, meaning that if you miss any of the balls, you'll have to start the entire level over.