Here is the full list of all 17 Concept Destruction trophies - there are 2 bronze, 4 silver, 10 gold and 1 platinum.
Get all other trophies
Drive through one of the goal posts in "The Stadium"
Destroy car "TIFA X/2" using car "ZIP JX"
Drive on the roof in "The Plaza"
Survive over 3 minutes in Survival mode
Get to the paint zone in "The Rooftop"
Win the Championship
Jump and stay in air for more than 3 seconds
Hit the hidden ball in "The Stadium"
Drive over 5 minutes in Tourism mode
Get out of the arena in "The Bulls"
Destroy a rival car in Tourism mode
Get out of the driving area in School
Destroy 3 rival cars in a single event
Pass all school lessons
Pick up 5 batteries from other cars (it doesn't need to happen in a single event)
Destroy a rival car