Make sure you have The City DLC purchased, or that it's on rotation for free trial, and activated for the game.
In the City, there's a shop called the Menagerie. At the Menagerie you can buy pets that functions like Followers, and that give you nice bonuses and extra abilities. They cost 2 gold, plus 1 gold per pet you already have. But it's always random which pet you get, so it can take some time to get the two needed for this achievement.
There are other ways to get pets as well. For example, the "Loyal Friend" and "Racketeer" Adventure cards can both give you a free, random pet. And you're likely to encounter both these cards before you acquire both Terrence and Hopper.
Just make sure to use any opportunity you can to get more gold, as a lot will likely be needed.
This achievement took me about an hour to unlock, I think. I imagine it can take a lot shorter, and perhaps a bit longer. Using the Prophetess character can help get helpful Adventure cards faster.