The known Genus in the monster file appear to be grouped. Together with hints about data being obscured by poor handwriting it suggests the unknown ones belong to the group they are in:
Toxicala = Beast
Earthmover = Beast
Raging Windrider = Avian
Flying Storm = Drake

Within a genus the data is consistent with being ordered by size  suggesting:
Rimewinder <= Scary
Dull Viper >= Rinewinder, <= Scary
Peaksnake  >= Dull Viper, <= Scary
Wrathrope >= Peaksnake, <= Scary
Earthmover >= medium, <= legendary
Macrophant >= Earthmover, <= legendary
Flamu >= small, <= large
Puffdrake <= small
Sandcrawler >= Medium
Thunderclap Wyvern >= Sandcrawler

Sightings by biologists:
All times/During weeks 6-15
Cassowarrior 46/13
Cold Parrot 47/4
Downhanger 98/22
Dull viper 65/16
Earthmover 71/15
Flamu 53/12
Flying Storm 45/18
Macrophant 35/5
Northern Badger 77/7
Peaksnake 41/3
Puffdrake 33/0
Rimewinder 25/6
Sandcrawler 53/7
Thunderclap Wyvern 31/14
Toxicala 19/0
Wrathrope 41/8

So the Toxicala is the most desirable specimen for the biologists, followed by the Rimewinder, Puffdrake, and Macrophant. The Toxicala  and Puffdrake have never been seen between weeks 6 and 15. and the Rimewinder is quite likely to be a small beast. The name of the Macrophant together with it's position in the list suggests it is probably a large beast, suggesting this is the most desirable one to find on balance. During this time of the year in the past it has only been seen in the The Lordesteppes, suggesting that is a good place to go. Hunts in this location also seem to be more successful on average than the average hunt. Posion Plate armour from the Poison element has been used on more than half of the succesfull Macrophant hunts, suggesting that is the best choice for them. A sword with the wind element is the most succcessful weapon.


For the locations the biologists look for specimens the following stand out:
They enver go to the Devils Maw between weeks 37 and 39 or between weeks 46 and 49
They never go to Miresmouth Forest in weeks 13 or weeks 33-45
They never go to Scorchsan between weeks 1 and 6 and between weeks 46 and 52
They never go to the Lordesteppes between weeks 20 and 32, and also in week 52
They never go to Thunderwood Peaks in weeks 7-19

Looking though the hunters logs hunts suggests:

Hunts in the gap periods in Devils Maw are either unsucessful or yield a Sliding Queen Shash (only in the first period) which has a scary size. Possibly this is only present during these times and the ancient biologists were
to scared to got there then? That monster has not been seen anywhere else or at any other times which is consistent with this.

Hunts in Miresmouth Forest between weeks 33-45 are unusually unsuccessful. Maybe the biologists are avoiding it because of poor pickings. Or more likely the Legendary Crow That Breaks The Sky frightened the biologists off, The hunters never caught one of these outside of this window which suggests the crows may only be present during this time? The times at which the crows have been caught in the Lordsteppes and Thunderwood Peaks also correspond to time when the biologists don't go there.. No crows were caught in Scorchan during the gap, however it they are migratory birds that are always present in one location then the gap would perfectly align with the time at which their location was not otherwise known, suggesting the cause of this gap is the same.

There is a clear seasonality with 

Winter= weeks 46-6

Spring=weeks 7-19

Summer=weeks 20-32

Fall=weeks 33-45

The biologists do not check Miresmouth Forests in the Fall, do not check Scorchsand Shores in the Winter, do not check The Lordesteppes in the Summer, and do not check Thunderwood Peaks in the Spring. There is also Devil's Maw which they can check year-round.

For all the species the biologists have seen tracks for, they are consistent either with being in one or more locations year-round or migrating between two locations, one in winter or summer and the other for the rest of the year. Note that the information can have gaps due to the seasonal non-checking mentioned above, so it might be that they really aren't all in these patterns, but I'm going with consistency.

The species seen are:

Downhanger (98 total). Migratory. Devil's Maw, wintering in Thunderwood Peaks.

Northern Badger (77 total). Non-Migratory. Scorchsand Shores and Thunderwood Peaks.

Earthmover (71 total). Devil's maw, summering in Scorchsand Shores.

Dull viper (65 total). Miresmouth Forests.

Sandcrawler (53 total). Scorchsand Shores, wintering in Miresmouth Forests.

Flamu (53 total). Non-Migratory. Scorchsand Shores and The Lordesteppes.

Cold Parrot (47 total). The Lordesteppes, summering in Thunderwood Peaks.

Cassowarrior (46 total). Scorchsand Shores, summering in Miresmouth Forests. Edit: incorrectly first wrote wintering here instead of summering, caught the mistake after finding Hunter data inconsistent with what I had written.

Flying Storm (45 total). Miresmouth Forests, wintering in The Lordesteppes.

Wrathrope (41 total). Scorchsand Shores, wintering in Devil's Maw.

Peaksnake (41 total). Thunderwood Peaks.

Macrophant (35 total). The Lordesteppes. Edit: migratory, summering in Miresmouth Forests. This was clear in the bio data but I somehow missed it when summing up and detected the omission from the Hunter data.

Puffdrake (33 total). Thunderwood Peaks, summering  in Miresmouth Forests.

Thunderclap Wyvern (31 total). The Lordesteppes.

Rimewinder (25 total). The Lordesteppes, wintering in Devil's Maw.

Toxicala (19 total). Thunderwood Peaks, summering in The Lordesteppes. I'm going on a limb on this one (since the Lordesteppes has no summer data, their tracks have only actually been seen in Thunderwood Peaks). But, they definitely are not found in Thunderwood Peaks in the Summer so for consistency with the assumed pattern I think they must be in the Lordesteppes at that time. 

todo: check Hunter data for consistency with this, plus learn more from the hunter data. 

The biologists have not seen tracks for: Sliding Queen Shash, Bull-King of Heaven, Raging Windrider, Crow That Breaks the Sky, despite these being included in their notes.

Unfortunately, the Hunter data also does not have any Toxicala hauls in the Summer, so the hypothesis that they summer in The Lordesteppes is neither confirmed nor refuted. All data seems consistent with what I should have wrote above (not necessarily with what I actually wrote pre-editing).

The Hunter data also has info on:

Bull-King of Heaven (Summer in Thunderwood Peaks, only 1 data point).

Crow That Breaks The Sky (Summer in The Lordesteppes, Spring in Thunderwood Peaks, Fall in Miresmouth Forests, Winter in Scorchsand Shores). Hmm. This is a familiar pattern - looks like the biologists' "ancient rules" are avoiding this monster for some reason. 

Raging Windrider (Scorchsand Shores and Miresmouth Forests).

Sliding Queen Shash (Fall in Devil's Maw, 2 data points).

The available diet data is compatible with the following rule:

Herbivores migrate in the summer, Carnivores migrate in the winter, Omnivores don't migrate and live in multiple zones, Scavengers don't migrate and live in a single zone. Hmm: to check - do omnivores really not migrate, or do they migrate at a higher frequency than the seasons? (edit: falsified: year 1 week 45 Flamu seen in both Scorchsands and the Lordesteppes.)

After some thought and analysis, after reading everyone else’s research, and in the absence of a more specific evaluation function to optimize for . . . I’ve decided to go all-out on trying to bag at least one Crow That Breaks The Sky. They’re confirmed to be big enough to make the Hunters happy, they’re something Biologists have never seen before, and they’ve been slain 8 times in 260 weeks by a Hunter who wasn’t specifically trying. We have ten chances, and can improve on those odds significantly.

Thanks to simon, we know they’ll be in Scorchsand for day 6 and Thunderwood for the rest of our allotted span. The problem thus reduces to “what weapon and armor should the Hunter bring?” and “what should she do once she’s managed to catch one?”.

Three of the eight successes were achieved with a Windrider Crossbow; three more with a Stormblade. Considering how many weapons were available, that doesn’t look like a coincidence. Of these options, I like the Crossbow better: a (weak, possibly spurious) correlation suggests Bow-type weapons tend to work better against Avians in general, and common sense suggests using ranged weapons against flying enemies is a more robust idea than hacking at them with swords.

Armor type doesn’t seem to matter here. However, I’m going to go out on a limb and say Ground Greaves, on the (ridiculously flimsy) basis that:

.The other Legendary and potentially-Legendary monsters she fought (Bull-king of Heaven and Sliding Queen Shah) were only ever defeated while wearing Ground Greaves, suggesting they’re good for fighting Big Things.

.The Crow That Breaks The Sky has an element of ‘Something Weird’, and the weirdest possible element for a bird to use would be Stone, so Stone-type armor might help.

.The Crow That Breaks The Sky has been defeated once before while wearing Ground Greaves, so this choice probably doesn’t guarantee failure.

When and if she manages to get a Crow, I’d advise her to move to Scorchsand Shores, so she can try for a Raging Windrider. This is also something fairly large which Biologists have never encountered before, despite it being fairly common (possibly because it doesn’t leave tracks?): seems like another opportunity to please both clients (especially since Hunters can make use of its body to make more Windrider Crossbows).

Spend Week 6 in Scorchsand Shores, and Weeks 7-15 in Thunderwood Peaks. When and if you take down a Crow, go back to hunting in Scorchsand Shores. Use a Windrider Crossbow and Ground Greaves throughout.

(This strategy will probably benefit the Biologists more than the Hunters, so be sure to extract gold and apologies from them when they’re gasping in amazement at the new specimens you bring in.)

Weapons are (almost?) always made from the corpse of a specific type of creature. Aside from 'Edged katana "Whisper"' and ‘Rock-on-stick’, it’s fairly obvious which weapons match to which monsters. This doesn’t seem to be useful for our main task – I tried and failed to detect evidence of a “ha ha, I’m hitting you with your family’s corpses!” bonus – but since weapon elements are always the same as the element of the creature they were made from, this lets us fill in some gaps in the Biologists’ knowledge. Namely: Dull Vipers are Stone, Northern Badgers are Cold, and Macrophants are Lightning.