I finally beat this ish (still gotta beat the neo bosses and I just started new game + though...addicted). I went through 150 kids basically spent half of those jacking up my stats and nerfing my guy without even bothering with bosses but I have some strategy advice for bosses if anyone needs help on a particular cat...
Khidr - Really it's just pattern recognition. I'd equip a dash rune or two and use a either a samurai or a barbarian (samurai's if you trust that you can avoid getting hit and barbarian if you're the opposite and want to try to rush damage). Don't guess, react...that's about it.
Alexander - Try to get a few vampire runes going in. If you can get the flames spell, it's really helpful too (if you have runes that sap mp and hp both it helps a lot). I did a lot of dashing from end to end and focused on killing the little guys with mana attacks. Don't get hit by the big one's orb attack (shouldn't be too difficult if you focus on that).
Ponce De Leon - You want a fast character and you'll want flight runes. Patience wins with this one (and the next). I made big sweeping circles from end to end, because it spread the flames a bit and left me room to turn back strike and run. The magic sword attack (where you place a big blade the shield you) can do a lot of damage here because he follows you. This was the toughest boss from me (final guys included but that could be because I grinded and leveled before them). In retrospect, a dragon may have been really good on this one but I used a hokage.
Herodotus - I honestly don't think this boss is THAT bad. I had a paladin with a dagger spell for him along with leeching (hp and mp sapping) runes and flight runes for mobility. The key is to not let too many enemies build up (which is why the dagger spell is useful, it won't hit multi-enemies). As soon as mages emerge, take them out. Try to get rid of the smaller blobs and get back to the big ones after you've eliminated the small groups. The spikes in the corners aren't so bad, just don't break the crates and use them as landing spots.
Johannes - You'll either want to max out a lich or use a barbarian bc you fight back to back bosses here. Don't waste all of your mp, he's not that tough. I beat him on my first try but wasted all of my MP and didn't have enough to rock with the Fountain after. Just avoid his mana attacks and strike when he gets close, having the sword (same as above) magic attack is really good against both the Fountain and this guy. I used a character with hypergonadism and a scythe attack to finally beat the boss combo, the trick was just standing in the corner and knocking him away as he closed in. From afar his magic was easy enough to dodge and when I finished him, there were still statues to break with some extra mp and health for the Fountain.
Fountain - By the time you reach him, his attacks shouldn't be that tough to dodge. He's huge and keeps coming forward so the sword attack or any launching attack (mana wise) is useful. Just be patient and avoid his attacks. He swings his sword pretty slowly so as he closes in you can rock him. There's no knockback when you hit him so that's good to keep in mind. Honestly, after beating the first four bosses, I kinda ran through the final two but I had OD'ed on leveling up my guys. Memorize what each motion he does means (they hint his attack and you'll want to know when the spear attack is coming) and you'll be able to handle dude.
Not many cats in this thread, but I used a lot of trial and error to figure these guys out so hopefully anyone struggling can just read these and get the help they need.