1 Batman is dreaming or hallucinating
All the events of the game take place inside a dream, or a nightmare, that Bruce is having. The fact that alarm clocks are heard throughout the game going off is a clue that proves that Bruce is dreaming. Some players suggest that he is having intense hallucinations while being awake.
2 Batman killed Nightwing
In the dream, Batman is the one who killed Nightwing. This was clear in the last scene where he realized that he was the one who killed him. Batman said that the killer knew how Nightwing fights and this also shows that it was him.
3 Batman was responsible for Robin's death
In the dream, Batman was also responsible for Robin's death, for he couldn't save him from Croc when it attacked him.
4 Batman was becoming dangerous
The full dream implied that Batman was becoming dangerous as a result of the hallucinations caused by the Joker's blood that went in his veins earlier in the events of Batman Arkham city.
5 Batman became overprotective in Arkham Night
The events of Arkham VR takes place before the events of Arkham Night. This was clear from the old suit model Batman was using in Arkham VR. This explains why Batman became overprotective of Robin in Arkham night. See also why Arkham VR is bad.
6 The radio scanner in the Bat Cave says wake up
There is a radio scanner in the Bat Cave. Once you turn it on it speaks out some numbers. When those numbers are converted to letters, you will get the words 'wake up'. This also shows that Batman is dreaming.
7 The game explained why Batman wanted to work alone
The game explained why Batman wanted to work alone later on in the events of the Arkham night game. After realizing he became dangerous, he decided to work alone.