The BCNM60 battles involves a face off against a "party" of named Beastmen.
There's 6 of them in total: Balga's Dias (Yagudo), Waughroon Shrine (Quadav), Horlais Peak (Orcs), Cloister of Tides (Sahagins), Sacrificial Chamber (Tonberries), and Chamber of Oracles (Anticans).
So far there are no BCNM60 for Goblins, Giants, or Demons. That may change (as there is a burning circle in Throne Room and probably one in Stellar Fulcrum).