Here is all that I have worked out for this mission so far using the fishing guide to see where the new fish are. If you all find out some more information on conditions to catch these, i'll try to add it on here.
Legend Name Location Skill Bait Weather Condition
La Noscea Endoceras Western La Noscea - Isles of Umbra Southshore 400 Fullmoon Sardine (Mooch) Fog Weather [Clea/Fair] -> [Fog]
Thanalan Kuno the Killer Mor Dhona- The North Shards 400 Assasin Fish (Mooch) [Gloom] Weather
Shroud Namitaro South Shroud - Urth's Gift 400 Top-Water Frog [Thunder] Weather + Buff from catching Giant Takitaro
Sky Shonisaurus Coerthas - Witchdrop 400 Unknown
Dune Helicoprion Southern Thanalan - Sagolii Desert 400 Storm Rider (Mooch) Weather [Fog/Overcast] -> [Heat Wave]
Sea Nepto Dragon Rhotano Sea (Sterncastle) 400 Northern Krill Rain Catch 3 Little Thalos for buff
