Boss cards can be obtained both in quest, dungeons and open maps
In quest, you get them from fighting bosses that you fight throughout your quests BUT not all bosses drop cards.
In dungeon, you just queue up the dungeon you want and fight the final boss within. Note that not all dungeon bosses drop cards and you don’t always get boss cards from the ones that do and may take you a couple of re-rolls from their boss cubes to even get cards.
In “open maps”, you get them from field bosses (like Dullahan in Roxona Consturction Map or Glackuman in 2nd demon prison). Theses field bosses are timer based and players frequently hunt them, so you have to be in a party to increase your chances of getting a monster cube from them.
Hope this helps