Namtar's Lair has been my PQI for a while.
For a while I just did flaming dungeons instead. Then I tried to tackle it a few times, but ran into walls pretty fast as I couldn't make barely a dent in the second form. I kept doing flaming dungeons to cycle the quest when I gave up. Purist Dwarf Wizard. Feeling Parched Dwarf Assassin. Purist Gnome Berserker. Purist is a killer, but at least it's cheap. A few I didn't try at all, like whenever I got Warmonger or Hoarder.
Today I finally got it with Faithless Elf Priest! I'm pleased, but everything about the run seemed anticlimactic, from the way the game dropped the Vicious-level PQI on me with no warning at all, to the lackluster gold reward. If the final locker slot is indeed going to cost 100K, I think a gold reward of several thousand is appropriate. Ideally, I'd like to have a "Vicious PQI" available parallel with "Normal/Hard PQI" so that if I just want a relaxing random challenge I can do it. Also, perhaps consider specifying either a class or a badge required, not both. Gnome Wizard Warmonger on Namtar's Lair is just not gonna happen.