Tropical Coast: Zone 3
Red Star Ring 2: After you finish the first side-scrolling segment, you'll pass through a corkscrew and then be confronted by several serpent-like enemies. Another Red Star Ring is situated on the red rail directly behind the second one.
Red Star Ring 3: During the second side-scrolling sequence, jump up to the top level when you get the chance; you'll know you're in the right place if you run into three golden mine carts. Continue along the upper level until you pass through a loop, after which you'll be able to leap and grab the third Red Star Ring.
Red Star Ring 4: When you run into the serpent-like enemies for the second time, hang an immediate right and jump to the green rail, which will launch you to the fourth Red Star Ring.
Red Star Ring 5: As you reach the fan blade at the very end of the level, you'll find the fifth and final Red Star Ring on the leftmost rail.
