Knights of Pen and Paper +1 Deluxier Edition

In order to get this achievement, you need to make one character of every class. You start with some : Paladin, Warrior, Rogue, Mage, Druid and Cleric. You can unlock Barbarian, Knight, Shaman, Necromancer, Witch and Hunter. The ones you unlock are unlocked via quests, though I wasn't smart enough to write down which ones. If you highlight a town via the map icon the % by the name tells you how many of the currently available quests there are, so if you're missing classes you can check for quests that way.

As for "playing" all classes, it's as simple as creating the character. You can do this by making a new game in an empty slot (or over a slot you don't need anymore) and then creating characters. You can make the first 2 free, and the next 3 cost 10, 80 and 250 respectively. To save money you can just make 2 classes, press select and then choose save and continue, and then make a new game in the same slot and make 2 more until you get this. That's what I just did.

TheOnlyMatto commented how to unlock the classes.

Sunset Castle has a battle quest that leads to knight class (may be a slay quest)
Sunset Castle has a slay quest that leads to the bard class
Yoga Village has a travel quest that leads to the shaman class
Default Village has a collection quest that leads to the hunter class
Default Village has an escort quest that leads to the necromancer class (ends after you meet death)
Journey Village has a delivery quest that leads to the barbarian class (ultimate weapon quest)

Dr B1ackheart said this unlocked before he did the shaman, and Pink Freud PhD said it was the same way for him.