Snowe’s Final Weapon
The Maiden’s Hope

This one is the trickiest to get because unlike the other ones, its side-quest can be started as soon as you get to the Eastern Tower (and is also the least obvious). Go through the door at the very top of the Eastern Tower’s stairway and in this room there will be a snaking hallway with maiden statues all over the place. Talk to the one right in front of the door and she will start off a story that she and her sisters want to tell you. Talk to them all in order and when you get to the last one through the secret passage, tell her to “Raise your voice.”

When you are allowed into the Forgotten Paths, go to the lone maiden statue relaxing all alone near a gate and speak with her. She has this weapon to give you.

Astra’s Final Weapon
Mistilteinn

This is the only weapon you can miss completely throughout the game. While on the Floating Isle, you’ll notice a sword in the Lord’s Tower behind a locked gate. It’s half of Astra’s sword and if you don’t get it before the Floating Isle falls, then it’s lost forever. To get it, once the party has been split up, once you leave the cells and enter the East Wing, you’ll see a line of doors. Go into the one with the banners on each side and that will take you to the Broken Sword.

Once you return to Sabine, give the Broken Sword item to Sharon in the Weapon Shop (you can do this as either Astra or Snowe, just make sure to give it to her before you finish up the Homebound Caves). Once you enter the Camp in the Homebound Caves, talk to Sharon again and she will give Astra the sword.

Hiante’s Final Weapon
Heroes and Villain

While in the Forgotten Paths, you can descend into the Forgotten Caves. While in the second set of caves, near the exit of them, you can hop from platform to platform toward a chest. Only you realize that a hole will upon up underneath you. Once there (you can also pick up A Fallen Soldier’s Memory from here as well), you can find a secret passage to the south of the grave. The pale gravel juts into a wall right underneath the steps and you can walk through that wall to enter another enclosure where the swords will be waiting for you. 

Relenia’s Final Weapon
Gungnir

This is perhaps the easiest final weapon to find and it can be found in the Western Tower. When you come across the puzzle in which you can change the lights on the bulb to make portals appear, make the light on the bulb white (which is to have red, green, and blue all on). Step onto the hexagram that appears and you shall be rewarded with Relenia’s final weapon.