The first two levels feature an enemy who mirrors your movement and you have to evade him. Then the rest of the levels lose the enemy and the game becomes a simple platformer.
Those are two game types each requiring different level design so you should first decide which model you want to pursue.
The jumping is okey-ish, I think you should not continue gaining moment/speed when jumping left or right.
You need more levels which should not take a lot of time seeing that you most likely use a simple software to draw them.
The game is totally silent, you need to have some sort of audio. Don't make the mistake of using a few seconds loop, it kills games.
Furthermore I would love to see some more objectives or perhaps pickups. The "get the key then exit the stage" will get old pretty fast unless you are a genius at designing levels.
I'm sure what the time limit serves here. The gameplay is very simple as are the levels. The limit does not add any challenge or meaning to the game itself. so I am not sure why you need it.
After you complete a level you should not be required to click to advance. If you feel the need to have that here at least let us press SPACE or a key.....we control the game with the keyboard after all.
Menu / level select / options etc need to be added but I guess you plan to do that.
Your game has potential, I really like the little guy you control.