PvE in Sword of the New World is essentially composed of Leveling, Farming, and, for most fun, Raid Bosses.
Once you have reached a sufficient level, you will want to try and get better gears to be able to compete against stronger bosses, or head for a PvP gameplay.
Raid Bosses Edit
Raid Bosses are very strong monsters that usually requires more than one family to kill them. They drop a lot of expensive items, but their spawn time is very slow compared to usual dungeon bosses.
For more information see Raid Bosses.
Special Events Edit
Poison Yard: Although this event is a mix of both, it has a great PvE side consisting of killing strong bosses (Recommend Veteran+).