As you progress through Story mode you will periodically be given weapon test assignments. When Story mode has been completed you will have had acesss to the whole arsenal of Hero Weapons to play in single-player mode.
Hero Shot:
Complete Lair 1.
Hero Roller:
Complete Lair 4.
Hero Dualies:
Complete Lair 5.
Hero Charge:
Complete Lair 6.
Hero Slosher:
Complete Lair 10.
Hero Splatling:
Complete Lair 13.
Hero Blaster:
Complete Lair 19.
Hero Brella:
Complete Lair 20.
Hero Brush:
Complete Lair 22.
To then unlock these weapons in Multiplayer mode you must complete ALL 27 lairs and five Boss fights in Story mode with a single Hero Weapon to unlock it. This means you must complete ALL 27 lairs and five Boss fights in Story mode nine times to unlock ALL nine Hero Weapons.
In order to unlock a single Hero Weapon for online use must beat every single Lair level in the single-player Story mode using only that one Hero Weapon. This also includes Boss levels.