To access the Intelligent Monster's route (name might change in the future), you must have Julia with you in her Normal personality and lose two battles against normal monsters and two battles against any of the Monster Girls (meaning you need to lose to Rubber Naga, Slime Girl, Flower Girl or Aquatic Girl).
After doing so, head to the Dungeon once more and wait around for a bit. Julia will then speak to the Protagonist and ask if the Protagonist thinks some of the monsters are different compared to the others. If the Protagonist agrees that some of them are, in fact, strange Julia becomes relieved and says she plan on trying to find out what exactly causes it. Otherwise, Julia gets annoyed at the fact that the Protagonist is seemingly too dense to realize this.
Shortly later, Julia remarks that the monsters are seemingly avoiding them. She asks for the Protagonist to humor her. If the Protagonist refuses to, it annoys her.
If the Protagonist agrees, they walk around and Julia notices that the monsters are stalking them while also keeping out of the way. The Protagonist becomes curious as to how that can happen, which causes Julia to say that they're intelligent so they're probably going to jump on them once they're weakend.