It turns out that the list of The Callisto Protocol trophies won't actually include one that asks you to die in every possible way. The full list of trophies for the game has been leaked, and that trophy, which garnered no small amount of controversy on announcement, is absent.
Back in August, Striking Distance Studios' Mark James revealed that The Callisto Protocol would have a trophy for "seeing all of the deaths". James said that the game's deaths are its "signature", and that they're not a punishment but a chance to learn from your mistakes and enjoy some "tongue-in-cheek entertainment" at the same time.
Now, however, it seems that the "see every death" trophy has been quietly dropped from the list. Striking Distance hasn't officially announced its removal from the trophy haul, but since the confirmation of the trophy came from interviews and not official studio PR, that's arguably to be expected.

You can see the full list of Callisto Protocol trophies right here (thanks, PSN Profiles). Be warned that there are spoilers for the main game's plot in there, and although they're not too big, if you don't want to know anything at all about The Callisto Protocol, it's probably wiser to avoid the trophy list.
Although no official reason was given for the trophy's removal, said trophy did receive some negative feedback from players, who said that obtaining it would be tedious or that The Callisto Protocol's high-quality graphics would make watching every death feel too gruesome.
It's fair to say this is a horror game, so some amount of gore should be expected, but forcing your protagonist to die over and over again might tend towards the overly voyeuristic. It's also hard to imagine that this isn't the kind of thing The Callisto Protocol's developers were put through 100-hour work weeks to achieve, so celebrating it feels just a little gauche.
You'll be able to check out The Callisto Protocol when it launches on PC, PlayStation, and Xbox on December 2nd.