It's possible to climb vines without the powerup by pressing the down key. I thought it was just a weird control scheme at first, but it turns out it was a bug.
Overall it's quite a well put together game. There are lots of adorable little details, like how the slimes still sit there and blink occasionally even after you burn them (though it sounds horrific when I say it like that).
However, the boss slime is a bit of a let-down. It's designed such that when you jump over it (or next to it), there's always a high random chance that it will shoot fire in a pattern you can't avoid no matter what you do, causing you to die instantly at no fault of your own. In general, putting an extremely difficult section right at the end of an otherwise easy and laid back game is almost always a bad idea, as it will just serve to frustrate and alienate most players. Especially in this case because, as far as I can tell, the boss seems to be invincible. If it's not, then give it a health bar, or at least some indication that I'm actually doing damage.