You have a really nice start here. I am liking the gameplay overall, but I think there could be a few improvements. It's really hard to stop the player when you're running, and it's very easy to overshoot platforms, which I did over and over again.
Some of these problems could actually be helped by level design. For instance, I was jumping across the moving platforms and reached this spot, only to miss the ledge and fall through the gap in the platforms. Then I would have to go all the way back up just to try the jump again. And again. It was painful:
If you just put a wall there you can keep the player from having to climb all the way back up if they miss. Making things easier for the player like this in the first level would help a lot. Allow the player to make a few mistakes without getting punished to hard, at least until they get used to the controls.
Another thing that would make playing a lot easier is MORE CHECKPOINTS. In the first level you should have a checkpoint after every difficult section, not after every four difficult sections. For instance, you could use a checkpoint at the top of that platform where I am jumping up. You could use another one immediately after the part where you need to sprint across two big gaps with the gem in the middle. When you reach the first checkpoint, and then have to go down the small spike section, then have to jump across two spike gaps, then have to climb the ladder with the spikes, then have to swim in the fans.... that's way too much to have to do over again when you die. It the checkpoint is WAY too far back.
So be nicer to your players on the first level. You are an expert at your game, but other people aren't, and a new player might get frustrated and quit playing because they have to do the same things over and over again just for making a simple little mistake.
I also think that it would be useful to add some camera controls to the game, so that when you're standing on the ground you can press up or down to look up or down. There are a lot of blind jumps, and it would be nice to know if I am about to jump down onto spikes. Also moving the camera out in front of the player when he is running would be a good thing, so you can see what is ahead of you better. He moves so fast that it's hard to react quickly when an obstacle approaches you. And it's not too hard to set up a camera that moves out in front of the player a little bit when he's moving.
As for the graphics... I really like the platforms and environment stuff. It has a really nice vector-graphics look to it. The player looks nice and is nicely animated, but it (and some of the other sprites) doesn't really match with the background style. It's more like pixel art. You might consider making all the graphics elements match up.
Also, I would like it if the game started in windowed mode and had an option to go fullscreen if you choose. Having it fullscreen glitches up on dual monitors when I click on another program.
Overall though it is a very good game so far.