Here is the full list of all 13 My Universe - Interior Designer trophies - there are 9 bronze, 3 silver and 1 gold.
Obtain 3 stars in all missions
Reach agency level 10
Complete all missions
Obtain 1st place in the LiveDesign ranking
Reach agency level 2
Meet all regular customers
Exceed the score of a competing agency
Obtain 3 stars on a mission
Complete a mission
Choose the name and logo of your agency
Unlock 30 decoration items
Discover a secret objective
Decorate a house in creative mode