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