Here is the full list of all 37 Time Machine VR (EU) trophies - there are 18 bronze, 14 silver, 4 gold and 1 platinum.
Obtain All Trophies in Time Machine VR
Reach the True Ending.
Complete 100% of the Dinodex
Complete All Of The Monoliths
Complete the Dinodex entries for all of Story and Exploration Mode's creatures
Complete 9 Dinodex Entries
Complete 9 Monoliths
Investigate the Neoparadoxia's herd structure.
Find out what happened to the Megalodon that attacked you.
Investigate the creature that saved you from the Megalodon.
Complete 7 Dinodex Entries
Complete 7 Monoliths
Find out why there is a lone Hesperornis
Investigate the veteran Elasmosaurus
Sate the Mosasaurus' voracious hunger.
Complete 5 Monoliths
Complete 5 Dinodex Entries
Complete 3 Dinodex entries
Resolve the mystery of the smaller bites on the Lusotitan
Complete 3 Monoliths
Create a new couple in the Dakosaurus group
Investigate the Titanites further
Complete your first Monolith Entry
Complete your first Dinodex Entry
Escape your first Monolith
Discover Your First Monolith
Help the Baby Pliosaurus find its mother.
Investigate the Ophthalmosaurus further
Return to any level in Exploration Mode
Complete Story Mode
Complete Level 4
Complete Level 3
Annoy Rob with the Mosasaurus' help
Complete Level 2
Unlock the Dinodex
Complete Level 1
Complete the Tutorial Level