In an attempt to make the most RNG part of the entire game even slightly more consistent, this is what I came up with.

1. Start the "Mini Game" Holding the Acceleration button.

2. As soon as you start moving, Tap left to start moving up-screen for around a second.

3. Tap right to straighten yourself out (your position should now be halfway between the line you started on and the top wall)

4. Keep your D-Pad neutral and just as you reach the clown he will turn up and land a solid hit on you which will send you backwards and point you downwards

Note: If you are pointed up after being hit OR if the clown just drives straight as you again you were too high or too low when he hit you or you didn't neutral the D-Pad.

5. Hold Left and straighten your self out so you are driving straight to the right

6. If you did it correctly, the clown will shoot backwards and down, then immediately start driving into the top, right part of the wall repeatedly.

7. Turn yourself when you reach him so you time it to drive straight up and bump him into the wall (For anyone who doesn't know, knocking him into the wall takes extra damage from the Clown)

I may mess around with it more to see if I can manipulate him a little more but so far this seems really consistent. To the point where I always get the first hit and sometimes am even able to get a 2nd hit.

The rest of the mini game is pretty normal but you get to start with a solid chunk of his health gone AND you know where he's at instead of driving into him at full speed and guessing where he went.

Good luck! Let me know if you have any questions!