The New Horizon update has added 4 new expeditions and removed the time restraints so this should be relatively easy with an end-game character.
The expeditions are as follows;
Molten Depths
Unlocked automatically
The Marshal's Complex
Unlocked at Challenge Tier 4
City of Nomads
Unlocked at Challenge Tier 8
The Wellspring
Unlocked at Challenge Tier 12
EDIT: If you are struggling to find players for these runs on TrueAchievements I'd suggest giving the Outriders Discord channel a go as I was able to pick up 2 players at 7am in the morning who were willing to help me with the Wellspring.