If I remember that place correctly you have to shoot the elevator motor with the REC to raise it, then you have a small window of time to grapple to the immovable elevator below it. That gave me a little trouble too.
Lol, I also had trouble there. Go into detective mode where the elevator shaft was, and you should be able to see an electric generator. Equip the electric bolt thrower thing, hold L1 and press R1 twice on it to make it go up two floors; this will give you a small window of time to grappel up.
\m/ RIP Ronnie James Dio, July 1942-May 2010. I hope you enjoyed your unparalleled musicianship while it lasted (all 67 years, dude). \m/