u/Drepanum

So, this image shows that I have beat (with the monk) the spider boss and the throbbing king on crazy difficulty, the rift and the coven at hard difficulty and the creator and dybbuk at normal difficulty.
My question is: Do all the badges automatically update into their ultimate version once I beat a boss at the "impossible" difficulty? Or to get the maxxed out version of a badge I have to beat the same boss once at all difficulties? Anyone knows? Becuase I'm trying to understand whether I want to do every boss once with each class before upgrading difficulty or if I can skip that