Here is the full list of all 35 Fallout Shelter trophies - there are 20 bronze, 10 silver, 4 gold and 1 platinum.
Collect all other 34 Trophies for this Trophy.
Successfully stop 50 Raider Attacks
Complete 100 objectives
Craft every Theme
Collect 20 Legendary Outfits
Complete 100 Quests
Collect 20 Legendary Weapons
Scrap 500 items
Collect all Fragments of 4 Theme Recipes
Complete 60 Quests
Build 1 of every room type
Level up a Dweller from Level 1 to 50
Craft an Outfit, a Weapon, and a Theme
Make 25 Babies
Collect all Fragments of a Theme Recipe
Level up a dweller from Level 1 to 25
Collect 100 Stimpaks and 100 RadAway on Quests
Upgrade 20 Rooms to Level 3
Make 25 Dialogue Choices on Quests
Complete 30 Quests
Kill 500 enemies on Quests
Change the appearance of 10 Dwellers in the Barbershop
Kill 10 Quest Bosses
Build 50 rooms
Successfully complete 50 Room Rushes
Complete 10 Quests
Craft 10 Outfits
Craft 10 Weapons
Collect 10,000 Caps
Level up a dweller from Level 1 to 10
Build 25 rooms
Merge 3 Water Rooms
Collect 1000 caps
Merge 3 Food Rooms
Merge 3 Power Rooms