Volgens TrueAchievements:
The Fragment of Invincibility and the Ochu Fragment sidequests become available after you have defeated the three Gigantuars. These can be battled by activating the Cactuar statues that do not teleport you back to the Nomad camp. 2 of these statues are the 2 rightmost on the Clearwater marshes and the other one is located in the Stonestump Wastelands standing in the midst of all the rocks.
If the Fragment of Invincibility and the Ochu Fragment sidequests do not become available immediately, return to the Historia Crux and re-enter the Archylte Steppe, they should be available now.
The Long Gui Fragment can be obtained as soon as you have completed all the main storyline objectives in the Archylte Steppe. Although I would not suggest you try to obtain this Fragment right after you have cleared the Archylte Steppe storyline objectives.
As for the Yomi Fragement ( at the time of writing this, the entry there is blank ), this Quest can be obtained from Tipur after you have obtained the Ochu Fragment. You have to change the weather to Stormy to spawn the Yomi. You will need to jump from the cliff to the south of the Waypoint with a Chocobo and fly to the waypoint. If your map of the Archylte Steppe is stuck at 99%, this will be the spot you probably will be missing. As soon as you hit the waypoint, you will dismount automatically. This is a difficult battle and best to be left until you have a reasonably leveled party.
