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 at all, sadly, which totally sucks.
Talk to Oggbi in Port Bastok (Steaming Sheep Bar) and he will give you the Trial Knuckles and a "writing of practice."
As I understand it, you participate in "300 points worth" of skillchains - points gathered by performing WS's on enemies that are Easy Prey and tougher to remove the weapon's latent effect.
Normal WS 1 point Lv1 skillchain 2 points Lv2 skillchain 3 points Lv3 skillchain 5 points
Then the latent effect is removed, it still appears on the item description, but it wont activate anymore.
Once you have cleared the weapon,return it to Oggbi and he will give you the "map of trial". Go to Bostaunieux Oubliette and find a ??? at I-8 by the Groundwater Way. Fight an NM called Bodach, then click on the spot again (as usual) and you will get the "writing of a trial". Talk to Oggbi to finish the quest.
The same galka who gives you the AF quests, Oggbi in Port Bastok, gives you this weapon for the quest "The Walls of Your Mind" which is the Asuran Fists quest. You must be L71 and have H2H over 250 to get the quest.