It took me a while to complete this but I did it with DH and used a lot of corrupt cards. You gotta use them before they are “corrupted” which is annoying as hell, but notice it says the word “corrupt” which means you gotta use them before activating the keyword.
That is an instant re-roll for me. So is the "play an old god 10 times" (I don't have any old gods). Any BG quest is my other auto re-roll. But you can re-roll every day, so you are bound to end up with something reasonable eventually.