Here is the full list of all 31 Square Heroes achievements.
Host 20 Internet games with remote players
Score Devastation
Score three Kill Streaks in a match
Score two Kill Streaks in a match
Score Mega Kill
Score Multi Kill
Win DM using only Explosives (3+ players)
Win without anyone else scoring (3+ players)
Score a Kill Streak
Score First Kill
Host an Internet game with remote players
Score Double Kill
Play entire round without dying (3+ players)
Complete Tutorial
Survive Survival!
Kill with Proximity Mine
Kill with Laser and Machine in round
Win 5 games in a row
Re-gen your health twice over
Re-gen 200% Team health
Replenish 150% Team ammo
Capture Gnome opponent almost captured
Complete 5 LAN games
Complete 100 games
Win team game 4+ players with 75% or more of team score
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Kill with Cross-bow and Harpoon
Kill opponent with Nuke Bag
Kill with Fire! (Flamethrower and Molotov)
Earn all other Achievements
Capture 15 Gnomes