When Bell fought the monster on level 18, he was so much out of its league that I figured that would gain at least two levels. But no, he stayed level 2.
To level up in Is It Wrong to Pick up Girls in a Dungeon?, you have to be on an "adventure." An adventure was never properly defined but it was presented as winning a tough situation that needed you to go 110%. When Bell fought the minotaur, it was way stronger than him but he made it, so he leveled up.
Then, why didn't he level up after the fight on level 18?