Here is the full list of all 14 Supersonic Acrobatic Rocket-Powered Battle-Cars trophies - there are 11 bronze, 2 silver and 1 gold.
Earn all of the stars in single-player
Score 500 goals in your Online career
Complete the Tournament Challenge
Earn a total of 100 stars in single-player
Earn a total of 75 stars in single-player
Win 50 Online career matches
Earn a total of 50 stars in single-player
Score 3 goals in an Online match
Score a goal while reversing in an Online match
Play 10 Online career matches
Achieve the Most Valuable Player award in an Online match
Win an Online match
Score your first goal in an Online match
Earn a total of 25 stars in single-player