All of the unlockables related to the classes themselves are all done via Quests from the Quest Shop. The majority of the Humanoid ones will require you to unlock a previous class for the Quest to appear, but the Monster-related ones are all unlocked as you progress in the main story. For the Humanoid unlocks, you will notice that there are descriptions to get a Brawler, Fighter, Mage, or Healer. The following explains which classes those terms refer to:
There are three major areas in the Disgaea universe, Celestia, which is home to the angels, the Human World, and the Netherworlds. The Netherworlds are split up into a bunch of different ones, each governed by an Overlord, who has their own set of rules. Those very same Netherworlds are now in danger of being destroyed or taken over by an evil army known as The Lost, who is being led Void Dark. However, a ray of hope appears in the form of Killia, who seems to have a deep grudge against Void Dark. Can he really go through the rumored 10 billion Lost soldiers and exact his revenge against Void?
Let us guide you on the epic journey from Level 1 to Level 9999, as you shoot, punch and fry enemies with various skills in our Disgaea 5 comprehensive guide!
Detailed strategies on getting through the main story;
How to get through the postgame content, including beat the super optional boss;
Create and power up a character that can deal in excess of 10 billion damage;