You need to complete Green Hill Zone Act 1 (Classic Sonic) from start to finish without losing any rings you collect along the way. Whether you collect 1 or 100 it doesn't matter, as long as you don't take damage and lose them. Just take it slow, rushing can have you running into things you didn't see coming. I've included a video below by jmm546. You may not have to take it as easy as this person but at least it shows you what to look out for.