There should be + buttons near the stats in the inventory screen when you have enough exp :3
So I had over the required exp, like 170/80 was what it said, but turns out, I just needed to defeat a slime to level up, so I think you can't level up defeating the dummy, you just get the exp, more and more exp, but you actually need to defeat a slime or maybe some other monster to level up. Is that intended or just like a glitch thingy? It's fine if it is a glitch or whatever, the game is still incredible ^^ Also is the demo/this part of the game over after the letter was delivered?