I’m confident that I completed all of the required tasks for the achievements, but something strange happened with six of the seven remaining achievements.
Winning with an ally was unlocked by completing a challenge, queuing five vils gave me the trade route one, creating a trade route gave me the automatic exploration one, ordering automatic exploration gave me the loom achievement, researching loom gave me the “win at Co-op Tours” and winning at Co-op Tours gave me the “do a challenge” achievement.
The only achievement that I have still yet to unlock is the one for queuing five vils.
I believe this issue may be due to the fact that the language I have configured the game to is not English.
I will try again later with a normal skirmish instead of custom map (I tried it and no achievement was unlocked).
EDIT: Grammar
EDIT 2: My hypothesis was correct.
I won a skirmish 2v1 and the “Queue 5 Vils” achievement was unlocked.