For this achievement, you only need to start a round, or take control of each of the game's six heroes from the base game. You do not need to complete a round of HvV at all for it to count.
In any multiplayer game mode that features a hero, either pick up a token in a mode outside of HvV, or select a hero in HvV and as soon as you take control of the character your achievement progress will track.
For the light side, the heroes are Luke, Leia and Han. For the dark side the heroes are Darth Vader, Palpatine and Boba Fett.