The tutorial dialogue at the beginning was a fantastic idea. I should have taken a page from that book with my submission.  I think the basic framework has potential if the mechanics are presented in a reasonable order and the level layout is accommodating.  There are a lot of areas where this could use some improvement, so I'll try to break this down:

Movement

• It wasn't clear to me at first the acceleration really picks up after a few seconds, allowing you to clear massive jumps WITHOUT running. This or running (via shift) was introduced as a requirement in level 3, though the awkward enemy placement made that discovery a bit tedious.
• I think level 1 should have more runways/less pitfalls to allow for playing with these more basic mechanics. Level 1 taught me that running is generally a bad idea where as the night city level taught me blindly jumping into the abyss was good.
• I was also a little hung up on the first platform because I didn't know I could double jump!

Collision

• The hit boxes in this game are entirely too big. Usually one of the first things I do in 2D games is try to find a way to gauge my character's (or whatever it may be) collision bounds. I'm not 100% sure how big the enemies hitboxes are, but I suspect they exceed the sprite and the player character's far exceeds the sprite. This makes navigating even the still enemies incredibly difficult.
• Here's me standing on a ledge, to give an example:

Visuals

• The render cells for the player are a bit off. You can see the right hand in the picture above wraps around to the left.
  
• Platforms blended a bit too much into the background on the snow level
  
• The BG elements on the cave level had me impulsively trying to land on them, even after I learned otherwise.

Over all, I enjoyed this game and again I think it as potential, if you decide to build off of it.

My favorite parts are the transition from level 1 to 2 and the upwards drift on the last level.