Here is the full list of all 16 Concept Destruction achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Survive over 3 minutes in Survival mode
Get out of the driving area in School
Drive over 5 minutes in Tourism mode
Destroy a rival car in Tourism mode
Drive through one of the goal posts in "The Stadium"
Pass all school lessons
Hit the hidden ball in "The Stadium"
Jump and stay in air for more than 3 seconds
Destroy car "TIFA X/2" using car "ZIP JX"
Drive on the roof in "The Plaza"
Win the Championship
Pick up 5 batteries from other cars (it doesn't need to happen in a single event)
Get to the paint zone in "The Rooftop"
Get out of the arena in "The Bulls"
Destroy 3 rival cars in a single event
Destroy a rival car