Go to Sierra 117 - Blind Skull on any difficulty.

With the Assault Rifle and a Pistol, keep shooting the Arbiter with the Assault Rifle until his shield decreases and then shoot him with a Pistol (in the head).

He should die at the moment you shoot him. Now you will see an Energy Sword which was with the Arbiter all along.

Quickly take it and then you will see that the Enery Sword is different from other ones.

I think this works in other levels, however Sierra 117 seems to be the best map to take Arbiter's Sword.