1 Batman killed Nightwing
It can clearly be concluded from the last scene that Batman killed Nightwing. Batman also added that the killer already knew about Nightwing's fighting tactics, which states that it was him.
2 Batman is dreaming or hallucinating
Bruce was sleeping, and every event occurred in the game, actually seen by Bruce in his nightmare. It is proven that he was dreaming since all the events were taking place as the alarm's sound can be heard throughout the game going off. Some fans of this game contradict this concept and believe that Batman is intensely hallucinating.
3 Batman was responsible for Robin’s death
In the dream, Robin was attacked by the Crocodile, and Batman was unable to save him. (See Why Do We Like Superheroes?)
4 Batman was becoming dangerous
Batman was becoming deadly and full of threats due to the hallucinations created in the events of Batman Arkham City. All this was caused by the Joker's blood that went into Batman's veins. (See Why Playstation 4 is good?)
5 Batman became overprotective in Arkham Night
It was pretty evident from the old suit model that Batman was using in Arkham VR, which is why he became overprotective in Arkham Night.
6 The radio scanner in the Bat Cave says wake up
Another thing that manifests Batman is dreaming is the Radio Scanner present in the Bat Cave. It gives some numbers as soon as it is turned on. Eventually, the numbers get converted into alphabets that provide us with some words; that is 'Wake Up.'
7 The game explained why Batman wanted to work alone
Later on, in the events of the Arkham Night game, he decided to work alone when he realized he became menacing.