In the map you can press 元 / Left Stick to see how many crew challenges there are per area. Crew Challenges: Crew Challenges often drop Eridium as a reward, especially Hammerlock’s Legendary Hunts (they are marked with green icons on the map when you’ve uncovered the entire map).Circles of Slaughter: Beating Circles of Slaughter drops some Eridium.While this isn’t repeatable, it does give you some Eridium passively without having to go out of your way. Story & Side Mission Rewards: Some missions will also give you the occasional Eridium reward.
However, they don’t drop that much more Eridium than the Crystals you find around Pandora and require much more work to kill them (they are pretty strong compared to normal enemies). After defeating them they turn into an Eridium Crystal which you can melee. This is the easiest way to farm Eridium but it still takes a while to accumulate large quantities.
Just drive around in a car and watch out for the purple crystals.