To get loads of Rings, you need to go to Arsenal Pyramid, playing as a Wolf with a Lightning Wispon, i recommend the one that gives you ring for beating enemies.
When you begin the stage, go to the upper route and jump during a ramp filled with Rings. After the Double Boost section, fall inside the Pyramid and collect the Rings. Once you see the Lightning Wisp Capsule, collect it and use the powerup by pressing Y or Triangle, and you'll go to a ginormous trails of Rings, skipping most of the stage and finishing with a max of 999 rings, repeat this until you get the achievement