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