Here is the full list of all 36 Cannon Brawl trophies - there are 19 bronze, 12 silver, 4 gold and 1 platinum.
Defeat Insane AI in Battle vs. AI mode without using shields.
Win against the Insane AI by selecting the warhead as your only attack building (Banks count as an attack build).
Win 5 ranked games in a row.
Destroy 1000 buildings.
Win a ranked game.
Build 1000 buildings.
Rank up to Admiral.
Defeat the enemy airship on nightmare mode.
Rank up to Vice Admiral.
Defeat the enemy warship on nightmare mode.
Destroy 500 buildings.
Earn 57 medals.
Defeat the enemy robot boss in Campaign mode.
Build 500 buildings.
Destroy 250 buildings.
Rank up to Captain.
Reflect your laser off two enemy shields to damage another enemy building.
Build 250 buildings.
Defeat the enemy airship boss in Campaign mode.
Rank up to Commander.
Reflect your laser off an enemy shield to damage another enemy building.
Rank up to Lieutenant.
Rank up to Ensign.
Defeat the enemy warship boss in Campaign mode.
Drop the enemy HQ in the water.
Damage Shield Towers 5 times by shooting around their shields.
Upgrade buildings 10 times.
All Trophies Collected.
Rank up to Grand Admiral.
Complete the campaign on nightmare mode. You did it!
Destroy 4 buildings during one blasting of the Flame Thrower.
Destroy 5000 buildings
Build 5000 buildings.
Win a total of 20 ranked games.
Win a total of 100 ranked games.
Reach 1500 rating in ranked games.