Here is the full list of all 30 Square Heroes trophies - there are 12 bronze, 12 silver, 5 gold and 1 platinum.
Earn all other Trophies
Replenish 150% Team ammo
Kill with Crossbow and Harpoon
Kill with Fire! (Flamethrower and Molotov)
Win DM using only Explosives (3+ players)
Win team game 4+ players with 75% or more of team score
Score Mega Kill
Play entire round without dying (3+ players)
Score three Kill Streaks in a match
Score Double Kill
Score First Kill
Complete 100 games
Capture 15 Gnomes
Capture Gnome opponent almost captured.
Hosted an Internet game with remote players.
Kill with Laser and Machine in round
Hosted 20 Internet games with remote players.
Kill opponent with Nuke Bag
Complete single player
Re-gen 200% Team health
Score Devastation
Score Multi Kill
Win without anyone else scoring (3+ players)
Score two Kill Streaks in a match
Re-gen your health twice over
Complete Tutorial
Kill with Proximity Mine
Score a Kill Streak
Survive Survival!
Win 5 games in a row