Dark matter

The Key To Farming Dark matter in FFXIII
Shao Long Gui. THey will be the bane of your existence if you do not have a properly formed party. Party should be Fang/Light/Van, with Fang leading. Have a triple sentinel for defending against ultima, and have Fang and Van equipped with a fully upgraded Moonbow Anklet, which gives them a 60% resistance to Daze, which it the enfeeblement that happens if he uses Screech on you. This will enable you to go into COmbat clinic with Light as a Sentinel, and Van and Fang as healers. Start in Tortoise, he will either open with Ultima or Quake. And until you have Protectra up his stomps will do massive damage. THe moonbows de-fang this otherwise powerful adversary. As soon as you get past his first attack switch to SUPERIORITY, which is Fang as a Sab, and both Light and Van as Synergists. Click abilities and spam Slow on him, then auto-hinder until you are fully buffed. You can spam Curse after you have Shao Long debuffed, which will freeze him until attacked. Now the fast part, if your timing is good and you are a bit lucky you can kill him without screech. NOTE Both Fang and Light should have Kaiser or Power Gloves equipped (one each) and a Genji Glove). Light will cast Enfire, and with the Bravara and Genji + Kaiser, your melee should do over 300k per hit after you have staggered him with triaster, AFTER he has been debuffed. If he casts ultima immediately switch to turtle (SENT SENT SENT) then switch to combat clinic for a rapid heal. Some people recommend THREE healers, but this can be dangerous, if he stomps or casts quake you need that AOE damage protection while healing, its more defensive. Go all out offensive and if your timing is right you can ravage his HP and when his Stagger bar is getting low (less than 10%). Use Fang's Command Super Move, HIGH WIND. It will do 999,999 damage, which is 10% of his total hp. If he screeches your veil OR your Moonbow Anklets SHOULD absorb the daze effect, which will otherwise destroy you after maiming your hit points. The moonbow is extremely helpful because it will prevent yur party from being debuffed entirely which is what happens if his screech hits you successfully. A 60% chance of blocking daze (screech) should be sufficient for both or either Van or Fang to be unaffected. If you are unable to kill him after one stagger, go back on the defense as briefly as possible, buff back up while spamming curse with the Sab/Syn/Syn discussed previously, try to get all buffs up and all of his debuffs down. It's worth a libra your first fight. You can get better common drops from much easier enemies (Admantoise or Admantortoise) but they do rare drop Dark Matter which is a huge time save on a couple of upgrades. Otherwise these enemies are useless to fight, except to say....I can beat the most powerful enemy in the game. IMO Shao Long Gui are harder than Long Gui, because you can incapacitate them for most of the fight.
Hope this guide helps. I haven't heard anyone discussing the Moonbow Anklets, which can be upgraded from a starred Rainbow Anklet with a Pervoskitite catalyst (sp)
Let me know how this works out for you guys! Make sure both Fang and Light have Genji and Power/Kaiser Gloves! If you are being hardcore you should get dual kaiser gloves, one for light, one for Fang!
Paradigm set up with Fang Leading! (Fang/Light/Van)
Aggression: Com/Com/Rav (Use this after his stagger has gone over 700%, if you are in the clear finish him off with this, note, use Highwind if he is about to recover from Stagger, it will do 999,999 damage and likely will kill him)
Tri-disaster: Rav/Rav/Rav (Use this as soon as your party is BUFFED and the Shao Long is DEBUFFED, spam magic attacks until his stagger is at 700 or so percent)
Superiority: Sab/Syn/Syn (USE THIS IMMEDIATELY AFTER HIS FIRST ATTACK. Select ability and slam him with slow until it sticks, switching to combat clinic if HP get low.)
Tortoise: Sen/Sen/Sen (Switch to this when he casts Ultima or even Quake, Bay is very hard to time, so just use the Moonbow Anklets)
Infilitration: Sab/Sab/Sab (Only use this if Fang hasn't completely debuffed the Shao Long, the debuffs that affect him are de-shell, de-protect, de-environmentals, slow, and curse, which will daze him while buffing. If Fang does not debuff him competely switch to Infiltration for RAPID Sabotage)
Combat Clinic: Med/Sen/Med (use this to heal inbetween phases, this is the Paradigm that will save your life! Note both your healers have MOONBOW ANKLET to protect from screech which will not only destroy all of your buffs but also cast daze, which makes your characters unable to do any actions.
If you do not finish him in time, he becomes extremely hostile and will combine Screech attacks with Ultima, and will respond to any aggressive movement against him with an Ultima attack. At this point the battle will be almost impossible for you to complete, as you will constantly have to change to tortoise and then combat clinic. Add to the frusturation, he will then DOOM your lead character. This battle can only be won decisively if you are fast. Have a maxed out Crystarium and elite protection accessories as well as the ones described. Good luck and have fun kicking the butt of the most powerful enemy in the game!