From bg:
1. Requirements:
Seidr Cotehardie 100,000
All Sauromugue Expeditions Completed to Goal 3
Thats actually not trivial, and will take a very long time. You get one pheromone each day, it would take 25 pheromones to clear all missions (or 20 if you dont need to clear the boss to meet this requirement, but idk). If you have 9 pheromones stored, it would take at least more 16 days till you can meet this requirement, suposing you can clear all mission up to 3 in first time (its not that hard, provide you have a good movement speed buffs/gear).
2. Farming marks is time consuming but the good thing is that you can repeat the same mission over and over, and it would take at most 15 mins each. The marks given scales with party members, so the more the merier. High level expeditions net more marks, but it doesnt scale with dificult proportionally, so even at rank 3 missions it should net the same amount of marks. Suposing the last expedition, you can net 3000 marks commpleting solo goal 3 (it would take 33 days to farm 100000 marks) or 4800 if your party has 6 members.
If you have friends willing to help, you can try doing this one:
https://www.bg-wiki.com/bg/Associate_Researcher_Expedition_4_(Sauromugue)
I never needed to farm marks (i got them eventually by trying orumilla), but according with the description:
Goal: opening chests (like abyssea pyxies, but if you miss all atempt, it spawn a mimic and reward no marks).
20 coffers worth 150 marks
8 coffers worth 400 marks
Solo, you have a multiplier 1, so you max is 6200 (but its unlikely to open all alone).
With 6, the multiplier is 1,6x so thats 9920, resulting in around 10 days worth to farm.