Tips for Eye Beam
Tip: Before starting a fight with the boss, make sure to collect all five keys that you can keep throughout all your attempts. This will give you a better chance of success.
So, the eye boss is a one hit kill on you UNLESS you have 5 keys, and go UP to the top of the wall (or at least the end of the game up top). The keys get used and defeat the boss, then you can get a win (though it’s pretty lame and there’s no real explanation or anything, so hopefully they work on that).
Just to be clear, there seems to be no way to win by going DOWN the wall. I’ve made it to the end, and there’s just water there and you can’t move further. So it seems to simply be a dead end.