Since Nick goes to the elevator to save Gus, so he must have noticed the "elevator killing" page from Catherine's book. Thus, he must have known that Catherine is the killer. Why then did he shot Beth?
Who convinced Beth to be at that hotel at that time?
According to Wikipedia:
Beth unexpectedly arrives and explains that she received a message to meet Gus. Nick suspects Beth has murdered Gus and, believing that she is reaching for a gun, shoots her, but discovers that Beth was only fiddling with an ornament on her key chain.
Why Beth is there? We can only rely on what she said.
When I first saw Basic Instinct, I thought "it is a simple story, Cat framed Beth" but after seeing it recently, now I see there was a murder coven and Cat wanted out. Nick had no idea, he was played by all of them in a twisted fantasy game.
Spoilers for Vertigo:
So it plays like a happy ending version of Vertigo.