Minfilia starts the chain to unlock these fights with the quest "A recurring problem".
After that is the quest "Ifrit Bleeds, we can kill it" to unlock Ifrit HM.
Clearing Ifrit HM unlocks the quest "In for a Garuda Awakening" to unlock Garuda HM.
Clearing Garuda HM unlocks the quest "In a Titan Spot" for Titan HM.

You can check the Chronicles of New Era-Primals section of your Journal to see if you've already done any of these quests.