This art style is absolutely gorgeous. It's clear you've put some real work in here, and I really want to see more.
The controls need a lot of polish unfortunately. The jump feels super floaty, and it loses momentum if you're up against a wall when you jump, meaning I couldn't clear small changes in elevation sometimes causing me to die. I would look into GMTK's tutorials regarding what makes a jump feel good. It would definitely help you
The axe climb feels a bit janky. I think you'd be better off only having the axe stick you to walls, and allowing the player to jump from there similar to wall jumps in a Mario game for example.
With the slime chase, I think you could improve the sequence if instead of having the slime balls on a timer you had specific parts of the level that just before the player reaches them gets slimed, that way you don't have impossible scenarios where a breeze blows the player across the slime into a closing mouth. Can't wait for the slime to dissolve or you'll get eaten by the slime, can't go forward or you'll die to the mouth trap
Also, I would really appreciate a small visual queue just before the spikes emerge from the floor, that way I know when to time my jumps if the spikes come on screen while they're in the floor cuz then I can't just use timing since I don't know how far into the sequence they are.
Regarding dialogue, all the keys for the controls are bound to left handed keys (WASD, Space, and F), so having to reach my right hand to press the enter key feels very awkward. Would recommend changing advance dialogue to space
One last thing, with the music, the music for the chase sequence is wonderful, but while it's thematically appropriate, the short loop in the rest of the level gets tiresome after a while. It's too short and starts to slowly drive you mad after a few deaths
I really can't wait to see how this improves. The art style is amazing, and with polish I'm sure the rest will be too