When the race begins after you talk to R.C., immediately get in front of him. If you stay in front of him while you race, he will bump into you but not go ahead of you. Do that the entire race to defeat him without the Rocket Boots. Also, if you make a mistake and he gets in front of you, do not stop the race - in some parts R.C. also makes mistakes, giving you another chance to get ahead of him again.

In Andy's Neighborhood, you can defeat RC Racer without the Rocket Boots. Stay directly in front of him, causing him to bump into you, which will keep him behind you. Be careful in the sand traps. Do not jump too high, or he will sneak under you, and if you do not jump at all, he will run over you.. Stay in the middle of the road so that you can cut him off each time he tries to pass you.