Lava Mountain: Zone 3
Red Star Ring 1: At the very start of the level, you'll come to a fork at the metal grates. The right side is guarded by spikes. Take that path, jump over a couple of platforms and find the Red Star Ring at the top.
Red Star Ring 2: In the zone's second 2D segment, you'll come to a point at which you'll need to dodge spiky balls on conveyor belts. Look for the Red Star Ring in the wall on the right side. There's an entrance to the hidden path directly below it.
Red Star Ring 3: After defeating the zone's second boss, the Red Star Ring is hanging between two massive, vertical grates directly in front of you. You get reach it either with skilled wall-running between the two grates of with assistant from one of the floating power-ups in this area.
Red Star Ring 4: Immediately after the last one, you'll find two more vertical grates with another Red Star Ring suspended between them. This time, you can use the jump pads in the area to start a successful wall-run and grab it.
Red Star Ring 5: At the very end of the final 3D segment, you'll pass through an area in which many large cannons are firing at you. The Red Star Ring is atop the second-to-last cannon on your left. Use the jump pad on the cannon immediately before it to launch yourself over.