Hey, thanks for playing! The level ups are determined by success in combat. You gain attack experience every time you successfully land an attack, you gain defense experience every time you successfully block an attack, and you gain speed experience every time you successfully mitigate damage. So basically you level them up by fighting enemies where you're able to flex your relevant stat! Stronger enemies give more experience, and you also gain more experience for having a higher mastery so if you get a few mastery levels you will be able to level much faster on subsequent runs.
We discussed a few ideas for decluttering the text log, but the most time efficient was to add color highlighting to "important" messages so they don't get buried. I wanted to make messages gradually get more transparent until they disappear but I didn't have time within the jam period unfortunately. It's definitely something we will be looking to improve if/when we update the game further!
Thanks for the comments!