The "unique" weapons are sometimes the rewards for a Gold Star on a level. When on the level select, you will see what the rewards are for each difficult and whether it's a Blue or Gold star reward.
- Blue Star: Complete the Level
- Gold Star: Complete the Level without the Hero (Librarian) taking any damage
For the most part, these are the extreme challenges, but there are a few that will unlock with the 2nd difficulty level.
There is also one weapon you need to buy in the last "town" of the game. The Evni Sword costs 500k Scrap so you'll need to save quite a bit. To make this easier:
- Turn up the Scrap bonus to 300% in the Options menu and turn down loss penalty to 0%. This will help the grind go much quicker.
If you're doing this on a Hero Mode run of the game, you'll likely be saving a lot more scrap since you won't be purchasing as much equipment and won't be purchasing new recruits.