Fragments of the Past, part I [combat (voluntary)]
Start: Old box (“Inspect”), at LOC: -1506,190, in Southern Jedi Ruins (Blackguard section inside long building), on Mustafar.

Part 1: Crystal splinters - Combat: Spawns 2 Trinity Assassin (CL83 Boss Jedi); Walk around LOC: -1500,235 until you get the popup message that says the splinters are humming; Search the area for some “Crystal splinters” LOC: -1490,253 (/target crystal); Radial menu: “Gather up splinters”

Fragments of the Past, part II [combat]
Start: Continuation of “Fragments of the Past” quest

Part 1: Reunited? - You have to find 4 Shard splinters around Mustafar (in any order). In order to do this you must first get a “humming” popup message and then a “Splinters awake” task, where you must search the nearby area for a splinter. This process is repeated for all 4 splinters. One is found on the ground, for the others you must defeat bosses to get them.

Shard splinter 1: Humming message LOC: 2176,3068; Find the splinter on the ground at LOC: 2135,3161; Radial menu: “Gather up splinters”

Shard splinter 2: Humming message LOC: -1447,412; Combat: Defeat Xos (CL88 Elite Jedi) [-1407,340] for splinter

Shard splinter 3: Humming message LOC: 1020,955; Combat: Defeat Magma Horn (CL82 Elite Tulrus) [998,1012] for splinter

Shard splinter 4: Humming message LOC: 3344,2880; Combat: Defeat Phantoms Bandits (CL69) in the area around the escape pod until you get the splinter

Part 2: Splinters awake - Need to complete this part for each of the Shard splinters

Fragments of the Past, part III [combat]
Start: Continuation of “Fragments of the Past, II” quest

Part 1: Assembling a crystal - Enter the Old Research Facility at LOC: 2109,3104, an instanced dungeon with plenty of CL80+ droids and creatures in it (see “Maps” links); Proceed through the dungeon as follows (use “/target” to find objects):

Main Floor:
1) Power Access Terminal (“Activate Power”) to open the door to the 1B Floor
1B Floor:
2) Storage Chest (“Open”) for the Access Key Card
3) Door Terminal (“Use Access Card”)
4) Journal Screen (“Inspect Closely”) for the Security Code
5) Door Terminal (“Use Security Code”)
6) Security Station (“Override Security”) to open the doors on the 2B Floor
2B Floor:
7) Photon Fusion Welder (“Start fusion process”)
Part 2: Process under way - Wait 10 seconds for the fusion process to finish

Part 3: Finished - Access the Photon Fusion Welder again (“Retrieve crystal”) to get the reward

Reward
Wild Force Shard (Defensive Burst) (blue)