I'm ashamed to say that I have no idea what the hell I'm supposed to do
D.
You don't have to somersault over every hole in the floor. If a gap is no wider than a lifting platform, try stepping across it. But don't let up on the joystick until you get to the other side, or you'll fall.
If you have to cross a very large chasm, you can actually have one foot in the abyss before you press the fire button to jump. If you do this just right, it will give you the extra distance you need.