There might be more than 2 new classes.
The two classes featured are 剣闘士 (Gladiator) and 砲撃士 (Explosives user).
The gladiator is a sword art expert, and has a skill (zenkiri) that attacks all enemies in a turn. He has another skill (kouretsugiri) that hits back rank enemies for the same amount of damage as front rank enemies.
The demolition expert uses a canon as the main weapon. One skill (gousei) allows combination of ammo and other items. Another skill (hougeki) uses up ammo to damage the enemy.