OK, just finished the fourth world. First off, the tutorial section there was flawless. You get introduced to the ice floors and walls before there's any spikes and it's pretty much impossible not to see how they work as you try to go through them naturally.
The ice was really fun to play with. The floors really get you nervous if you start going fast on them. And I like how you can shoot up the walls if you keep jumping at them. Really fun set of levels!
Only major gripe was that I flew into the exit on 4-4 when I was trying to climb up and get to the secret. The exits for levels should be detached enough from the rest of the level that you can't accidentally hit them.
For making the flower icon more clear, you could have some kind of particles going in the menus so there would be some immediate feedback when it's pressed.
EDIT: Played a little more. Level 5-1 was pretty fun! Having no checkpoints definitely makes you feel more tense as you start venturing into parts of the level you haven't seen.
5-2 made me ragequit, though. Made it a ways into the level and a turret I couldn't see sniped me as I moved to the edge to get a better view of where I was going. I like the way 'no checkpoint' levels feel, but they need to be fair for it to work.
Now that I think about it more, maybe just lowering the bullet speed a lot would be the best solution to making the turrets fair. As long as you can react to them, bullets coming from offscreen would probably be OK.
Anyhow, it's a fun little game and I enjoyed playing it quite a bit. Hope to see an update soon!