Uhhh...talk to that galka first in Mines, the one in the second floor and then go to PalMines. Find the boat NOT THE BLACK SPOT because that is the BCNM...although the boat is in the same map. Once you take the boat back to Zeuhn you will get the sword. Since you are WAR equip it and take out 100 enemies and go to beadaux and you will get the job. You might also want to kill and ADDITIONAL 100 enemies with the sword after getting the DRK sword as that gives you the lvl 5 GSword Deathbringer. Its not bad.

EDIT: Then again Vap, you can just borrow mine if you want it...