Swords
To obtain the Dabilahro sword, you must collect 20 Scarabs. You must buy the Wooden Sword from the merchant and then fully upgrade it by collecting Yellow Essence from defeated enemies and buying improvements from the merchant. When complete, the weapon will change into the Unlabored Flawlessness sword. Complete Chapter 14 and take the Kitetsu sword when you begin Chapter 15. To get the Plasma Saber, you must beat "Ninja Gaiden Sigma" on either normal or hard mode.
Nunchucks
Search the dead body in Chapter 4 to pick up the standard Nunchaku. Open the chest in the Tomb of Eons in Chapter 7 to get the Vigoorian Flails, which are nunchucks with blades.
Other Melee Weapons
Find and destroy the big pot at the beginning of Chapter 4 for a Lunar staff. Back track to the Monastery at the beginning of Chapter 10 to find a War Hammer. At the beginning of Chapter 13, inspect the dead body and pick up the Spear Gun.
Shurikens and Bombs
Open the chest in the altar at the beginning of Chapter 2 to get Smoke Bombs. At the beginning of Chapter 6, run up the wall with blue lines on it and jump on the ledge to get the Windmill Shuriken. Go into the Archive Room in Chapter 7 and search the area to get the Incendiary Shuriken.
Bows and Arrows
Find Ayane in Chapter 2 and get the Bow from her. Near the end of Chapter 10, defeat the soldier with the RPG launcher to earn the Strongbow. Play through Chapter 9 to get both the APFSDS Cores and the Explosive Arrows.