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