Dynasty Warriors 7

To unlock all weapons, you will be required to play Conquest mode. Some of them can be found through Story mode, but only about 40%.

Defeating enemy officers, either in Story or Conquest, provides a chance to get a dropped weapon. This isn't required to get them all, because eventually any ones dropped this way can be purchased instead.

Each weapon type has one weapon which is unlocked through a Treasure Battle. These are actually called "Treasure Battle: X" with X saying the weapon type, and are indicated by a hex with a sword and thick lines coming out of it. This is different from the hexes that just show a sword, which reward a random weapon you don't already own but don't award the special weaopns.

Each weapon type also has one weapon which can only be purchased from the Merchant or Weapon Dealer. This weapon requires the Smithing skill, which only a handful of characters have. If you've completed the Story, Zhuge Liang and/or Guo Huai (the guy with the arm cannon) will probably have the skill already based on how many skill points you earned during the story. This means you will need to switch to character with the Smithing skill prior to entering the town.

There are three weapons (Spear, Sword and Twin Swords) which require special objectives:
Answer all scholar questions correctly
Unlock all capital cities in Conquest
Complete all battles in Conquest

Any weapon that doesn't require a special condition or a Treasure Battle can be purchased from the Weapon Dealer or Merchant. Keep in mind the Merchant offers a significant discount, but is not always available in town. Hovering over a town hex will indicate if the Merchant is in the town currently, and he only offers a random selection of 3 weapons at a time that you don't already own.

If you're not sure which weapons you're missing or still need, an easy way to check is to use the Gallery and check the Weapons category.