Not sure if you can post amazon links so I apologize in advance.

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I'm a big fan of Odd Tinkering. It's not necessarily a step-by-step tutorial but you'll get the gist of it. Honestly all you need is some compressed air and some 99% Isopropyl Alcohol. I use MG Chemicals and transfer some to a dropper bottle. Grab an old toothbrush and start scrubbing. For the shell I use warm water and some dish soap.

The gamecube jewel badge on the top of the console is super easy to pop out in case you want to repolish it and buff out all the scratches. I use this stuff, it's meant for headlights but it will work on other plastics. Or you can go on esty and find custom jewels if you want to dress it up.