There are four classes to choose from (Warrior, Hunter, Assassin, Mage). For this achievement you only need to win with three of them.
There is no in game tracker that I'm aware of, so you need to keep track of which classes you have won with.
If you get knocked out but your team still wins, it still counts as a win for whatever class you were using.
Edit: The patch on 1/31/19 appears to have made it so that wins are no longer tracked and thus this achievement is not currently unlockable.
Edit: The patch on 2/12/19 seems to have restored tracking for this achievement. Unfortunately any progress made while the tracking was down will still not count.