My spouse and I had a lot of trouble getting this one. No matter what we did, we couldn't get any of the Alluring Specimens to count (or even find them easily). After a lot of searching the internet and finding a lot of other people having the same problem, I thought I would share what we ended up doing in case it helps anyone else.
First, go to the same system as Dropzone 4/Phase 4. (We found that it wouldn't work at all for us until we were in this system).
Do Dropzone 4 (and Infestation Delta if you want). The planet (Azuzuma F38) that Dropzone 4 is on has an ocean. Go somewhere that has a decent amount of deep water, as far out into the ocean as you can manage (the place I was had a LOT of small islands so I just chose an open spot in the middle of them).
Dive down and look at your scanner. You want to find the red Alluring Specimen pin. You might need to hunt around a bit to find your first or maybe you'll get lucky like me and your first is right where you land.
Head to it and you'll see a cup-shaped rock type thing. If it looks like this...
Note that it has several 'Anglerfish style lures' coming out of it (green ball things on the end of the curved line). You need to get close to it (don't worry nothing happens until you 'pick it') until it turns to E interact and then pick it a bit like you would oxygen out of hazardous flora. They gave me Hadal Cores.
The NMS style nightmare Anglerfish that comes out will appear on any of the glowing green ball interacts. It could appear on the first one you pick or the last. Be prepared.
We didn't find it particularly troublesome to kill. But it does get all up in your grill making it hard to shoot. You can use any weapon you want but I personally found the scatterblaster the fastest.
One you've taken down your first, you move onto the next red Alluring Specimen pin. The first one I did, didn't count but the second did. The only difference was that my spouse and I tried to take the first one out together.
The second one worked fine if we were more than about 150-200u apart. So this is something you should do either single player or at least separately if in a group.
The way we found the next Alluring Specimen was to go exactly North or South away from the one we found. I do not know if Alluring Specimens adhere to the NMS planetary ley lines but it's what I do anyway to find the same of something.
It took me about one oxygen refill (using Candle Kelp so I didn't have to surface) and/or a full jetpack boost before I could scan and see another red Alluring Specimen pin. Given that YMMV depending on modules, this may be different for you. The only modules I had were ones I picked up from milestones and along the way so nothing special.
At any rate, rinse and repeat twice after the first pin/specimen and you should have all three for the milestone to pop for you :)
Safe journey travellers!
Thank you so much for the detailed guide. Did this expedition on a whim (got a steam deck and was trying games) and I think I'm at dropzone 3 or so. I haven't touched underwater since NMS release, since I actually have Thalassophobia (fear of underwater stuff).
How spooky would you say NMS underwater is, and how deep is it? Because I've been avoiding it out of fear that I'll just nope out immediately.
For reference I can't go beyond the shallows in subnautica without panicking. Luckily, in NMS you can just shoot shit and its overall pretty easy so I'm less worried but trying to get a gauge on it so I don't have a panic attack.