How in the *seven hells* did Martyn learn these spells? [BLU Lv.50~60 SPOILERS]

[ReiMakoto]

Correct. The first Minstrel's Ballad was Ultima's Bane, then the Second Coil of Bahamut, Thordan's Reign and Nidhogg's Rage. ARR EX-fights are all 'real', a new incarnation summoned to be stronger than the last.

Back to Martyn: Well, he is the original Blue Mage and more familiar with the art of blue magic than we are. Maybe it's enough for him to just see or know about the attack to mimic the spell and he doesn't need to actually beat the Primal for it.

Martyn isn't the original Blue Mage the Whalaqee are, he just got the Blu soul crystals from studying them

Doesn't seem likely.

The "Soul of the Blue Mage" crystals were made by Martyn himself, based off what he learned from the Whalaqee over the New World.
And even then, I'd assume it's a similar process to what SMNs do to get their Egis/Trances/Demi-Primals (i.e. actually facing/defeating their originals).

If this is the case, his soul crystal could be different, maybe an actual Whalaqee one and not the new ones he made for others