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