good start, keep it going!
Alright you have potential here. Possible additions to make this game more challenging:
1. put a natural decline to peach's elevation as the level progresses, where you need to either be pushed up by intermittent gusts of wind, or press a button to gain altitude.
2. Put a pendulum motion to peach's neutral movement. When the player is not moving peach side to side, she should have a natural swing that takes her at an angle. This would make firing at enemies a bit more challenging and would add in a "timed shot" sort of element.
3. Power ups! increased movement speed, bigger turnips, mushroom, (make peach bigger,) Mini mushroom (makes peach smaller) points multipliers, 1 up mushrooms etc.
4, harder enemies, with more hits to fell.
5. Maybe consider putting in extra lives and reducing the health of peach.
6. More enemies. :) i got tired of seeing the same shy guy over and over. Even something as simple as color differentiation would give more flavor to the game. Perhaps bosses floating in hot air balloons? Lakitu is a natural air enemy from mario, as well as the Sun from Mario 3, Birds from mario 2, So many options!!!
7. Nthing sound changes for peach. putting in a little more differentiation keeps things from getting spoiled too quickly.
8. put some animation to the characters!!!! adding something as simple as a little wind ruffle to peach's dress or to her parasol to make us feel like we're floating and not stagnant. Enemy animations could just be flapping arms, to keep it simple.
9. Boo, a great idea for a boss. HOWEVER, you used him as the only boss and he was not challenging whatsoever. how about making it so that your shots phase through boo when he turns invisible?
10. Change the backgrounds every level! every time you defeat a boss, make a slight change to the background level to keep it fresh.
Overall, this was a well done framework for a game, but its not complete. I would love to see the finished product with a bit more variance. The backgrounds were well drawn!!