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