Here's a list of the Arkham VR trophies:

http://www.playstationlifestyle.net/2016/09/29/batman-arkham-vr-trophy-list-already-available/

Here I've posted it here if you can't access the link:

Bronze:

To the Batcave – Unlock access to the Batcave

A Death in the Family – Identify the witness

The Last Laugh – Identify the murderer

Bite-Sized – Discover doll-sized characters

Through the Looking Glass – Find and zoom view on the Mad Hatter cameo

Riddle Me This – Piece together Riddler Trophy, Cube, and Cane in Riddler Case file

Catch Me If You Can – Activate thrusters on Bat vehicle

Inside Out – Place the two lungs, eyeball, and cranium in to their correct locations in the anatomical model

Crime Never Pays – Score 30 or more on the Batarang trial

Silver:

Bad Blood – Analyze all five blood samples for infections

Bits & Pieces – Destroy all 18 CCTV Cameras, Fuse Boxes, and AR Batarang targets

Fallen Son – Analyze all four pieces of evidence from Batman’s past failures

Gold:

Knight Out – 100% the game. Complete the main story, find all Riddler secrets, and acquire all the trophies