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