Here is the full list of all 13 VR The Diner Duo (EU) trophies - there are 9 bronze, 3 silver and 1 gold.
Burn 50 burgers
Complete all tutorials
Complete level 15
High five yourself in customization
Complete the first tutorial
Customize both the waitress and the chef
Serve 500 burgers
Score 2500 points in endless mode
Throw a burger to a customer
Complete level 30
Get 3 stars on all winter levels
Unlock all customizations
Get 3 stars on all normal levels