EDIT: Some player wrote on September (2024) that this solution didn't work and the game was patched.
So I played the game to see if that was true. After 5 tries, I got 600 rings. I came here to answer to that player but he/she deleted their comment. I recorded a video showing that is still possible get 600 rings with Tails in this level.
I forgot to write on the original guide that you need fruit for every try on this level. If you don't have fruit, you can't play the level.
In this video (not mine), you can find where is the fruit in (almost) every level:
And remember: This guide is for tips and showing that getting 600 rings in this level is possible. Getting negative votes or saying that the guide doesn't work anymore when skills are involved, it's because of angry/annoyed players. If that were the case, I should give negative votes on guides for Metal Slug, Rock Band/Guitar Hero, Street Fighter, etc... -_-
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After spending almost 20 fruits on the first fruit level and without results, I found this video. Took me only 2 tries
(Press Factory Zone)
Use Tails, try to get every ring balloon and what you need to get without failing are the bonus rings for flip every circle with numbers. You can get hit by the lasers even.
(Credits to AMHarbinger)