I just figured out I need to press space to start the game. The game looks fantastic, and am loving the feel of the controls and the music. I would never have guessed I needed to jump on those enemies with a spike on their head though. The explosion doesn't fit the look of your game in my opinion. It would probably look nicer if they drop down off the screen.
Pulling a lever to reveal a platform in order to progress is cool and like that it is easy to pull it. I think there should be one at the very start just to make it clear this is what you need to do to progress even though this should be obvious. I think you got the right idea by keeping the enemies away from the levers. The levers could be more challenging to get to by adding things like spikes that protrude from the ground, and puzzles etc as the enemies are not too difficult to defeat or jump past. Not sure what you got planned with having loads of different types of enemies, but they could jump, have projectiles etc. I don't like how enemies can walk across the bottomless pits, they should either fall in or turn away. I ended up jumping into it thinking I could do the same thing!
Other than that, great job, and best of luck!