You will be required to purchase one upgrade from the black market as part of the story. You'll need to buy 4 more, which will require at least 16 Eridium since the cheapest items/upgrades cost 4 each. Completing missions, defeating bosses and searching chests will give you more Eridium. Further on in the story, at higher levels, you'll get Eridium more often, which will make it even easier to get the required amount for the achievement. You'll unlock this achievement once you have purchased a total of 5 items from the black market.