Ring King requires you to collect a total of 100,000 Rings. It countys all the rings you have at hand by the time you reach the end of the level. Granted it can take a really long time, so instead of playing through Green Hill a few hundred times, getting 200 or so rings every time, here's my method which gets 999 Rings every time.

Even though Steam isn't counting the total rings you have for the achievement progress when you check, the game is still counting it. So don't worry about what Steam is telling you.


Make sure you're playing as a Wolf race, as their ability allows you to draw in near by rings.
Also recommend you beat the game so you have the Void Wispon, it's helpful for dragging in a cluster of rings and getting rid of a horde of enemies.
If you don't have a Void Wispon, use a weapon that awards rings for defeating enemies.
Now just play through Stage 4, Death Egg, Prison Hall over and over again. Everytime I go through it, I get 999 Rings everytime, I make sure to hit all the ramps in the beginning and collecting every single ring on the way, but you don't have to, the level has enough rings to reach 999 anyways. Use the Void Wispon a lot to gather any Rings I'd otherwise miss. Once you get 999 Rings though, it doesn't count any rings collected afterward.
This is the method I used to get this achievement. I hope this helped!