NINJA GAIDEN Σ

The Kitetsu is a sword that shares a lot of the moveset with the Dragon Sword, with some unique moves that set it apart from its counterpart. In particular, Dead Soul Bind (X,X,forward,mash X) can be used to heal Ryu by draining the life from enemies, while being rendered invincible for the duration and Stab of Extinction (Y) where Ryu throws the sword like the Windmill Shuriken. It also has a different UT, which is superior to the Dragon Sword. It is obtained in Chapter 14, after Ryu defeats Doku in Chapter 13, the sword will be in the centre of Zarkhan Stadium.

Being similar to the Dragon Sword at level 3, it is preference which you use, though the True Dragon Sword being a level 4 weapon is superior. Kitetsu is often available in Mission Mode, sometimes instead of the Dragon Sword, so if you are aiming for a completion, you will probably pop this naturally.

If you feel or find yourself with the need to grind out the 1000 kills in Story, there are two spots I would recommend. Chapter 12 has a respawning flock of bats in the area with the Save Point and the manhole to Tairon and Chapter 18 has a group of 45 Ghost Fish that respawn every time you use the doors to the Stairway to the Imperial Palace. Pick a spot, tap away at X until each enemy is dead, then leave and re enter the area to start all over again.