Drop rate is estimated to be ~5% base. There's no pity mechanic so you're no more likely to get it after x attempts. The only ways to increase odds of it dropping are the specific triumphs that state they improve initial drop rate. I think they are tied to gathering the collectibles, a clear on master, and then solo / flawless / solo flawless. We also don't know how much of a boost these each give. We had to do ~45 runs for one of my friends to get it, it really can be a pain.