Is it somewhat Luck-Based? In order to finish it, All You need is just kill the Avatar, or do You have to kill You overpowered foe, too?

I beat it a few weeks ago, and it wasn't luck based. Enemy attacks are almost entirely controllable once you know what triggers them.

You must kill/convert the Avatar to win. I don't think you need to kill the enemy keeper to win, but I suspect you need to kill the hero dungeon heart. Killing all enemies is entirely possible (I did it). If you want specifics, let me know; I'll stop here in case you want to work it out on your own.