The levels are entirely possible, given the right approach, but they're certainly very difficult.
After the jam we'll make the game a little more accessible by making an easy mode, as its clear the extreme difficulty isn't for everyone. Also you are not able to hit enemies just for the fact that it'd make the game much too easy given the limitations of what we had to work with in the time given, this also could be something we change in a post-jam version, with a harder difficulty that doesn't have that feature.