More a tip than a full solution if you don't have friends to play with, as there is no custom game search feature, and you rarely go back to the lobby between levels:
If you join a game which already has 2 players of the same class in it (and you're a different class), take note of the gamertag of one of the players. Back out to the main menu quickly, change character and search for the player's profile on your xbox friends screen. Join the game off of their profile.
You do not need to play through an entire level, you can join at the last second and still get the achievement.
Too many times I was in a game with 2 others and I was a different class trying to get this achievement, and luckily this worked! You can also do the same for the achievement for using one of each class.