Originally posted by Frag__Hero
Will try to give what advice I can but time is also limited today.
What exact error message are you getting?
Pluwaka mentions needing "free DLC on store installed." You mention Judge Jury Executioner, but you don't mention the My2k Entitlement Bonus. That's also a free DLC and while it's not from the store, some of the content from that pack might be in this save. Basically, to get it, you need to link your copy of Mafia III to your My2k Account (create one if you don't have one already, then immediately edit the privacy settings if you care about that sort of thing).
Also, while this is technically paid DLC, a lot of people forget about the Family Kick-Back Pack. It's on the Store NOW, but wasn't for a long time, because it came with pre-orders only. If Pluwaka had a pre-order copy, might've slipped the mind. That sort of issue has arisen before. But before paying for more DLC, I'd exhaust all other option (unless you have the Deluxe Edition in which case you should already have access to this for free).
Putting ALL of that side, if you do have the 7.62mm and the Party Animal outfit, then my guess is this isn't a DLC issue. Double-check you're wearing the Party Animal Outfit while going for this. The only reason I'm mentioning that is because you're talking about going for it while going for the nuke, but I'm pretty sure your outfit is set during most of that and can't be changed so you wouldn't be able to get it then anyway. You can ONLY rack up kills for this trophy while wearing the Party Animal Outfit, which (I could be wrong) is only unlocked AFTER completing the DLC.
Another possibility is that the profile save you're using is already over the 50 kill counter for this.
So here's my recommendation. Get yourself in a place where you have both the 7.62mm equipped and you're wearing the Party Animal Outfit. Drive to Pastor Jerome's church and save there. Then, in case it is an issue with the profile (back it up first if you will need it after - sounds like you won't if this is your last trophy) delete your profile save so you're starting fresh at 0 kills for sure. Then drive to the police station in that same district (French Ward? whichever district Pastor Jerome's church is in). If you don't know where the station is, I'm sure you can find a video if you look up guides for pretty much any kill-related trophy because that's a famous farming spot.
When you get there, draw your 7.62mm BUT MAKE SURE THEY GO HOSTILE before you start shooting. If you start shooting before they go all Darryl Gates on you, then they won't count as "enemies". Gun down everyone in there and everyone who responds, but make sure eventually you let a couple of cops kill you. Dying auto-saves and so will save your kill count. You can get 20 or more right there, then respawn at the Church which is like 2 or 3 blocks away. Rinse and repeat. Should take 2 or 3 runs max. Way, way, faster than going through the DLC (plus I really don't remember being able to change outfits while going through the island part of the DLC).
Hope that helps.