Begin by boosting forward as Sonic. You'll immediately encounter several basic Egg Pawns. Use Sonic's Homing Attack (B button) to chain through them. After a series of loops and springs, you'll come across a section with floating platforms. Switch to Tails (Fly formation) to easily navigate these, using his flight ability to cross gaps and reach higher ledges. Look for hidden ring trails in the air.
Further on, you'll encounter a large stone block blocking your path. Switch to Knuckles (Power formation) and use his powerful attack (B button) to smash through it. Continue through the ancient ruins, utilizing each character's strengths. There's a section with a large water slide; maintain speed and jump at the end to reach a higher platform. Collect the first Special Key if you see it, as these are crucial for Chaos Emeralds. The goal ring is usually preceded by a series of speed boosters.