I finally did it. When exiting the exploding room remember this....
Make sure you have 300 health, that you are on casual, and watch the entire cut scene.... Time your jumps so that you never stop running... i.e. You can jump over most ledges
Use x for turbo until you get to the elevator... At that point simply use the joystick and a to jump back and forth up the elevator shaft...
My health was still at 280 as I started jumping up the elevator shaft. Before that I was getting stuck climbing over two ledges, one in the exploding room and one jumping off the ladder... Both ledges can be jumped over without stopping with good timing.