There are 11 weapons in Bastion they are all unlocked through natural gameplay, the final weapon is the Calamity Cannon and this will be found on othe mission where you rescue Zia (after the siege)[//spoiler]
by the time you find the final weapon you should have 2 or upgrades applied to all the other weapons at the point. if you miss collecting upgrade materials during missions you can buy them at the Lost and FOund Shop.
This achievement is really just one of patience,