Here is the full list of all 27 Smashbox Arena trophies - there are 10 bronze, 10 silver, 6 gold and 1 platinum.
Play on Every Map
Complete an Multiplayer Match (Online Mode)
Complete the Story Mode on Hard
Shoot 10 Times in a Single round
Complete the Story Mode on any level of difficulty
Score 3 eliminations in 1 Round
Block an Incoming Shot with a Ball
Eliminate the same Enemy 3 Times in a Match
Eliminate an Enemy 3 Seconds after Teleporting
Catch a ball, then eliminate an Enemy with it
Catch an Incoming Shot
Complete the Tutorial
Unlock all the Trophies in the Game
Play a Match as every Character (Original Cast)
Hit an opponent from over 30 meters away
Complete a match without being eliminated
Unlock all the Characters
Score 100 eliminations with Boulder Balls
Score 100 eliminations with Sniper Balls
Score 100 eliminations with Fire Balls
Score 100 eliminations with Heat Seeking Missiles
Score 50 eliminations with Grenades
Use Shields to Block 50 Incoming Shots
Win a Match 5-0
Eliminate 2 enemies with a Frag or Boulder
Score 1000 eliminations in Story mode
Score 1000 eliminations in Online Mode