At first I found this game very hard, but that was until I found out how useful F is. I even got the All hearts medal, which at first I thought was impossible.
For that medal, the best tip is: you just have to position yourself at the same height as your enemies (sometimes you'll need to jump) before they see you, and press F; the bullets will kill enemies even off screen. Doing this, you can kill almost all enemies without ever getting damaged.
For the high jumps that damage you when you land, just jump right before touching the ground. Kinda like jumping on a falling elevator right before impact, but actually working ;)
About the pit of lava in level 3, same as before: just jump before touching the lava, that is, as soon as your character enters the screen (since he'll be falling very fast).