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