Let's talk about Hunts - a detailed rundown of their assumed mechanics

[KageTokage]

Tried all of the following during a new moon with no luck:

Killing 30ish normal/naked yumemi.

Spearing 20 turnshells.

Three consecutive completions of the aforementioned FATE.

[Leonoire]

If you can gather some friends, try to do one thing in each instance next full moon. The timer was barely up due to the maintenance at the last new moon.

[KageTokage]

Other stuff that didn't work during a full moon:

Spearing 20 spiny lobsters

Clearing the Daimyo Yumemi boss FATE

[Vandesaan]

I read over the Japanese text for Okina again and it says 貝の死骸; every time I look for this on Google it comes back with seashells. In English they just talk about shellfish husks, but the Japanese definition (shellfish remains) just returns a bunch of seashells. Horned Turbans from spearfishing maybe?

[Leonoire]

This sea is just chock full of shellfishes if the definition below is right:

There are two kinds of shellfish: crustacea (such as shrimp, crab and lobster) and mollusks (such as clams, mussels, oysters and scallops).

Half of the mobs there are crabs and shrimps. Not counting the DoL/DoH stuffs.

[Vandesaan]

Overworld mobs that aren't tied to FATEs or player events in The Ruby Sea are:
Tatsunoko - flying snake thing
Gyuki - mammal
Unkiu - crustacean
Coralshell - crustacean
Bombfish - fish
Sea serpent - flying snake
Shiranui - flying squid
Flying shark - ...
Hellborn anala - humanoid fire elemental thingamajigger
Gasame - fire crab, crustacean
Red bukan - Kojin
Red hyoe - Kojin
Red honkan - Kojin
Striped ray - manta
Apa - elemental ghost things
Ruby hornbill - bird
Island gedan - hyena
Yumemi - snails, mollusc
Naked yumemi - snails, mollusc
various sprites - elementals

Based on the above description, the suspects would be Unkiu, Coralshell, Gasame, Yumemi and Naked yumemi. I've no idea how you narrowed down the suspects for Leucrotta, maybe this is something similar? All of the mentioned can be hunt bill targets too, just like the ones for Leucrotta. Looking at what the Japanese hunter crowd has been posting, they are focusing on fishing exclusively.

[Leonoire]

Tried a kill run on the 2nd day of full moon, no pop. Target was Unkiu, Gasame and Yumemi because JP names.

[KageTokage]

More things that didn't work during a full moon:

Killing 30+ Unkiu and Coralshell

Spearing 20 spiny lobsters and 20 spider crabs

Fishing up 10 fan clams

[TrollToll]

Just spawned on Midgardsormr. I was fishing at x13 x16 in the boat with live shrimp during a full moon. HQ Fan Clam was what popped it, I believe.

[KageTokage]

That's...odd.

I'd think it would've spawned after I had caught so many clams, but then again, I only caught one HQ clam, so that might have something to do with it.

That or someone else spawned/killed without notifying the linkshells/reporting it on the trackers.