Weapons are unlocked automatically as you progress through the singleplayer and co-op stories.
You will unlock all weapons attainable in the singleplayer storyline by the time you finish Michigan AVE. As for the co-op story, there have been mixed reports. I had only finished the first two co-op missions when I unlocked this achievement. Some say you'll get it by the third, though.
Note: It has been reported by some that you must pick up the weapons for them to count. This may be a glitch. I know for a fact that I never picked up the AK-47, or the SR-2M, and I still got the achievement. Those two weapons seem to be the issue, I never see anyone complaining that they can't get, say, the Scorpion. So if you come by either of those weapons, pick 'em up just to be safe.
The weapons required for this achievement:
SR-2M(Unlocked in Co-op, I believe.)
AK-47(Unlocked in co-op, I believe.)
AKS-74U (Unlocked in co-op)