Attempting to mine with DRG's Quest active, will mean you will obtain the Wyvern Egg first.
After you have collected all 3 key items, zone into Beaucedine Glacier for a cutscene.
You may receive this cutscene directly after visiting the Neptune's Spire, but you would still have to collect the key items in order to advance the quest.
Go to the small lake in the upper left corner of J-7 (near Fei'Yin) and click the "Mirror Pond" for a cutscene.
There are 2 "Mirror Pond"s. You want the northern one located at (J-7), not the one located at (G-10).
Head to Neptune's Spire and click on the first door to the left for another long cutscene.
Your NPC must be present and close to the spot when trying to obtain the above key items. If it's too far away you will simply do the action you normally would without NPC, therefore not getting key item. You can call your NPC with either a Signal Pearl or a Tactics Pearl. By now you should have high enough bond to have your NPC with you long enough to gather all 3 key items in a single use of either Signal or Tactic pearl (Be sure to have maps ready with harversting, logging and excavating points indicated).
Be careful not to get on a chocobo if your NPC is already out, as it will make him or her disappear. The points in Jugner and Shakhrami aren't far, but the run to Giddeus might require you to take a chocobo.
You can Teleport with your NPC.
Using Sprinter's Shoes is useful, but remember to wait for your NPC to catch up before trying to obtain the items. You do not need to wait up for your NPC to change zones.
You do not lose the tools when you receive the key items.
Fastest way seems to be find a point in [Giddeus] and summon NPC, [tele-holla] and do Jugner next, then finally [Tele-Mea] and finish in shakhrami.
