I got this weapon when i used a cheat engine to give myself the Bullet That Can Kill The Past when playing as The Paradox. As soon as i used The Gun That Can Kill The Past, the unlock message appeared.
random unlock[edit source]
yeah this thing is very bugged, i opened the ammonomicon randomly and got the unlock message.
I've never played co-op and I just unlocked it after getting the fourth alternate starter gun.