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