I don't see this mentioned here, but I just learned (since I needed 357 points to break it [and I got 57 points in Dynamis tonight]) that you cannot use your weapon and expect to gain points for it in Dynamis. They will not count towards your goal sadly.
Incase you've never seen this WS in use its awesome. theres a video of it if you go to vid forums at FFXIonline.com Basically you leap into the air and bring your GS smashing down on the mob. only one word can describe it... Hot!
I just finished this quest today. After getting the points and trading the sword to Gumbah, You go to E-9 of West Altepa Desert. Touch the ??? and the Tiger NM. A decent level 70ish party can take it. It's only like fighting the Tigers in Kuftal (Ovinniks)only with more HP. It might hit harder than the Ovinniks but I wouldn't really know since I had filters on and had a Ninja tank. Touch the ??? again after defeating tiger then talk to Gumbah again to get your WS.