Ah yes, I remember that one. It's very difficult. Only advice I can bestow upon you is to time your movements extremely precisely and in the part with all the elevators, right where the ceiling ends, jump up and there's a hidden block with a mushroom in it. It's very useful since if one firebar keeps killing you, you can simply run into it as Super Mario and run through while flashing as regular Mario.
______________________________
"Legolas is a guy?!" -My Sister