Well designed with smooth gameplay
Graphics worked well along with the sound. Gameplay was fluid and the game was easy to grasp. I don't want to be mean to the artist, but from a professional standpoint the weakest part of the game was the art in the art sequences.
Gameplay Suggestions
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I suggest that the radar show you the way towards gems you have not yet picked up. I'm sitting at 99.7% and can't for the life of me find the last few gems.
The air recovery should probably grant a brief window of invulnerability, because you can easily get yourself killed if you recover and immediatetly get hit again (the boulders falling during the nightmare boss, for instance.)
The pit at the bottom of the tower to the right of the sky sequence is poorly designed. When you have low jump and no double jump, falling down there is almost a guarenteed death, and that sort of "gotcha" design doesn't fit well with the rest of the game (even the lava, a traditional deathtrap, does only 1 to 0 damage.)
Also, I could never find the "dashing course" one of the medals refers to. Not sure if I just didn't recognize it or I never actually found it.
Bugs
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+I activated the computer around day 5. When I came back the next day (I didn't have 100%), I activated it again and nothing happened, except that I could no longer move my character and had to restart the game.
+I hit "restart" on the menu during a game where I had level 5 everything. I then went back to the menu and hit "load." The 5 graphics underneath your healthbar that fill with experience were uncolored, as if I were still at level 1, though I still had level 5 in the status screen and jumped/ran/etc at level 5.
+After hitting "load" same scenario as above, the character that fell onto the protagonist's fence was still in a lying position on the ground, though I could interact with him normally.
+The medals are not working.
Anyway, on the whole this was a great game. I'll be keeping an eye out for more of your work and good luck with the sequel.