Demon Partisan was surprisingly easy, although I forget whether I got it first try or took a couple tries, and what strategy I used. One helpful note is that it doesn't count against you if a demolitionist explodes a demolitionist or wizard with a bomb. I don't know whether if counts if you bashed the bomb, though.
For the speed run, I'm pretty sure that getting winged sandals from level 10 is required, but other than that I think it's more flex. If you pray at an altar, you can restore your energy by taking divine restoration, which helps offset the time penalty of visiting the altar. In my attempts, I've also grabbed 2 fortitudes from earlier levels, because otherwise later on I tend to die or waste a lot of time avoiding dying. Winged sandals eats a heart when you train it, so with no fortitude upgrade, you only have 2 hearts, which is pretty fragile. Maybe it's better though to just go without and hope for the best.