When coming up on said turn hit and hold the R button (the break) and hold the analog stick in the desired direction. This should make the character skid toward the edge and keep them facing the way you want them to go. Then just when they're about to go over let go of the R button and they should shoot forward, avoiding death.

It takes some practice but eventually it will become second nature and it's way more effective than pumping because you keep up the good speed.

Hope this helps.

You gotta pump and turn at the same time.

It also doesn't hurt to have a firm lead so you can start breaking a tad bit earlier than the turn.
I will admit, Babylon Garden is a mean one until you get through it the first time.
Good luck. If that doesn't work I'll run the level tonight to see if I can't figure out another way to get around it.
You should really ask my brother. He's psycho when it comes to that game.  o_O

I do beat him in the Egg Factory though.