I actually had to look up someone else's strategy, off Gamefaq I believe, to get it. To start you immediately jump on the moving platform and do a sideflip back to get the first present. Then, you get on the platform when it comes back, sideflip up to the second moving platform, and hit the yellow switch, immediately jumping back on the platform and then grabbing the key. Then, you drop down for the blue switch, use that, and that get back up to the second moving platform with the key. You then throw the key up to the platform above with the blue switch, get off on the blocks to the right, sideflip up to the top moving platform, regrab the key, and jump back on that platform in order to jump to the left uppermost blue part. Grab the present (use the key to help if needed), then time your jump down so you land on the middle moving platform. Then, hit the yellow switch and jump back on before it leaves again, and get to the door.
The second part is pretty straightforward, only things of note there are that you can jump straight to the ladder over the ghosts, you don't have to stop them, and the final jump can be cleared with a triple jump in its default position.
I remember all of that off the top of my head just due to the shear insanity of it all. They REALLY shouldn't have put such a ridiculously tight time on that level.
Thanks, I'll try practicing that. It's very frustrating because if you miss a jump you lose several seconds. Seems like the run has to be perfectly executed. Argh.