Midway Arcade Origins

For me, this was one of the hardest achievements in the game.
Like Oobgarm said, its not a good idea to start on the first ("easy") course.
The problem with doing so is that for the 3rd course, you have to play on a track which has 'shortcut doors,' which are extremely hard to maneuver through, and which the computer will take EVERY time they are open, putting you at an extremely unfair advantage.

SO, here's what I suggest: start on the bottom right ("medium" course). Make sure to avoid the medium course on the direct right.
Choosing to start on the bottom right medium track will give you 3 easier tracks, no trap doors. On the 3rd track, you will have a randomly-generated tornado, which is probably the only reason its categorized as "medium" and not easy, but it didn't cause me any problems.

Other than that, just familiarize yourself with the wanky controls and should get it eventually! don't give up!

Personally, I found this achievement easier if you select the second track to start on. That could just be me getting used to the controls, though.

It's a fairly simple achievement that just takes a bit of practice if you're having trouble.

Ah, Championship Sprint, here we go:

Step 1: If you have not yet popped any achievements on Midway Arcade Origins, remove the disc from your console and delete the game history. Break the disc and burn the case. Go play a game that doesn't suck total ass. Send me a "Thank You" letter.

Step 2: Fire up Score Attack mode. Choose one of the starting tracks marked "easy". They are both about the same difficulty. The default track features a slightly easier first and second track, with a harder third track. The other "easy" starting track features a slightly harder first and second track with a slightly easier third track. They are both miserable, but I recommend the second starting track.

Step 3: Learn the steering controls. Championship Sprint features a very unique steering system in that the steering controls are virtually non-existent. You can't actually steer per se, what you want to do is use the D-PAD (this is a must) to gently nudge your out of control vehicle in the right direction. Attempting to actually steer your vehicle will only result in frustration and anger.

Step 4: Learn when to gas it. The right trigger controls (kind of) your acceleration. You want to keep this pressed all the way down and let off just before a curve, using your momentum to nudge yourself around, before holding it down again. There are a lot of curves, so you'll more or less be pumping this as you play.

Things that WILL happen while playing Championship Sprint: (1) You will randomly explode. (2) The other cars will constantly run you into walls despite your inability to do the same to them. (3) You will lash out at your friends and family. (4) You will lose interest in a hobby you once loved, namely gaming. (5) You will curse Midway and wish physical harm upon everyone involved with this POS game.

Things that WON'T happen while playing Championship Sprint: (1) You won't have fun. (2) You won't get three wrenches before the third track, don't even bother.