My suggestion is to get yourself in a place to allow as many RNG benefits as possible for this one.
In completing quests for the Inquisitor (specifically selling burgers and beer at a witch burning), he'll then ask you to harvest dark organs. Once you've gotten the request for the three organs, you can go into the technologies and purchase the tech to do so - it's on the anatomy line, so depending on how many points you've saved up and what you need to unlock, this may be the first grind. The good news, though, is that each of the three dark organs can be studied for 150 blue points each.
Once you've unlocked the technology, you'll be after a dark brain, a dark intestine, and two dark hearts (the second dark heart is for a Snake quest). They'll show up randomly in new dead bodies you get. Load up the trough with carrots for the donkey and start hoping.
I read on the Graveyard Keeper wiki that the Prayer of Repose potentially helps the organs show up because you have more red hearts possible in each body. I crafted a gold prayer of it and tested it on and off, and didn't notice any great difference, but you're welcome to try.
Some people have said, on Steam, that they were able to dig up bodies with multiple red skulls that were already in the graveyard and had success finding a couple organs that way. I'd already cleared them out trying to appease Yorick, so I'm not sure.
Finally, I read a Steam user's post that the vampire hunter you kill as a part of Snake's quests has a couple dark organs. So if you haven't progressed on that side, lucky you.
In my case, however, it was a matter of checking each body when it arrived, grabbing out the dark bits if they were there, and hoping to FINALLY get the dark intestine I needed. Then it happened. So, random. The key to it all is to get in a position where the randomness can happen, so get that tech!
Once you turn in all three (and you can turn them in one at a time if you choose to), the achievement unlocks.