Hey, I tried the demo, and I love the style. I also like the way the challenges progress. If I may make some suggestions:
Maybe add some FX to indicate important events; for example, some kind of lens flare or hit effect when the player hits one of those ghost orbs, and maybe a color change or particle effect when the player is in the mushrooms that slow him down.
Also, I got stuck in the level with the rotating platforms; the third jump just felt a hair too far; I fell on it about a dozen times then gave up (of course, you might intend for the game to be really hard, but I kind of think there is plenty of challenge for this early in the game – assuming this is still intended to be the very first level.) Also, since you say your main intention is to tell a story, it is probably a good idea to avoid frustrating players, especially early on before they understand what is going on in the narrative so they get hooked.
All that said, your platformer is way better and more refined the one I'm working on, so take my suggestions with a grain of salt. Great work, especially with the minimalist art. Cheers!