There's no conventional level up in this game.One thing that has confused me is my Aura has had several different cursed items on her which only required days to remove so I had to put her to the side for a while but Tomo I've been using almost constantly is still only level 2. I didn't have any other cleric's until recently today since I've been using my mage as a backup healer so I know I couldn't accidently mix them up. Is it because in almost solely using heals with her and rarely attacking?
Characters level up by completing development goals (essentially: repeatable achievements) you can see in their profile, in the dungeon screen in the character/party tab and party bar to the right.
It's shit like "Start dungeon naked", "Kill/Defeat 10 goblins"("kill" require last hits, "defeat" is party-wide), "Complete Lab-type dungeon", etc. Also if the goals are ass*, you can reroll them in the character profile
Also when you are in the dungeon party selection window (i.e. when you click on a dungeon on the world map, then go to the character tab), the game will highlight any goals that are specific to that kind of dungeon for that particular character, if any. The others, well, you just need to keep track of mentally, but they otherwise appear in the right-most party tab in the dungeon.
* - for example I had Cowgirl Tomo with so much negative damage from quirks, that she was doing literally zero damage with every attack, so any goals requiring dealing damage were completely uncompletable.