It took 124 deaths but I beat the hard level! Great job, I was determined to finish and although it took me a little bit to get the hang of the controls it ended up being not too bad after a level or two. I would agree with some of the comments below to add maybe LMB/RMB to move left and right rather than clicking on the side of the screen, or at least showing somehow which direction you'd be moving in based on where your mouse is. However, I did like that because of the limitation, rather than give your character a bunch of different moves you incorporated the different mechanics into the level directly.
Nice work!