Sonic Adventure DX Director's Cut Tips

Another way to get rings in Adventure Fields
Playing with Amy (you have to have the Warrior Feather), in Station Square and the Mystic Ruins, use the Spinning Hammer Attack to cut the grass and you'll get rings. Oddly most sites don't mention this at all.

Playing with Tails on the Egg Carrier, when it's switched around, fly to the top of the giant spinning thing in front of where the pool area is (the white-roofed building).

With any character (except for Big the Cat), you can get rings from the inside of the pool area on the high platforms on the Egg Carrier.