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