This achievement requires you to deploy 5 units or "vanguards" with 5 different classes into battle.
Assuming you checked the "balanced start" box when you created your game, your starting heros should be made up of three classes; Caberjack, Hunter, and Alchemist.
There are 9 classes in the game, the 3 base classes and 2 "hybrid variants of each".
Hybrid classes are created by breeding 2 different class heros together in keeps.
The list of hybrid classes are as follows:
Caberjack(Regent) + Hunter(Partner) = Shadowjack
Caberjack(Regent) + Alchemist(Partner) = Blastcapper
Alchemist(Regent) + Hunter(Partner) = Boomstriker
Alchemist(Regent) ]+ Caberjack(Partner) = Brewtalist
Hunter(Regent) + Caberjack(Partner) = Enforcer
Hunter(Regent) + Alchemist(Partner) = Trickshot
So the fastest way to do this would be to simply build 2 keeps as fast as you can, than start breeding your classes, and waiting for your trainees to come of age. Then simply deploy 5 different classes into a battle and achievement unlocked.