I originally concluded after much experimentation that to get Astral Phantoms:
-You had to be on disc 2
-Received Protect Key #3
-Then proceeded to leave the map and pet your dragon a consecutive 6 times…
Well, it’s even simpler than that. After having done the exact criteria I myself stated, I didn’t receive Astral Phantoms no mater how many times I tried to pet the dragon. So, I began to level up. After each level I would pet the dragon once.
And at level 26 I received Astral Phantoms without having received protect key #3. So, there you go. I hope I can finally put this to rest.
-Name Your dragon
-Be on disc 2, at least to the point of entering Uru, level up to 26 and pet your dragon, and you will learn Astral Phantoms!!