Special Weapons are the weapons that you fire with the
.
Special weapons are rewards for meeting certain criteria. To make things simple, reward criteria come in the form of unlocking achievements.
Some achievements will unlock characters, but most unlock new special weapons. Once you unlock the required number of achievements to get 15 special weapons, this will be yours.
FYI, this achievement will actually unlock during play when you meet the requirement for whatever achievement awards the 15th special weapons. (So basically, you will get back to back achievements). You won't have to wait for the rewards screen.