My opponent moves a creature to a battlefield, they pass focus and I play a Pillaged Armory to the battlefield with Jarvan IV, Martial Paragon activating Jarvan IV, Royal Heir ability to pay a power to move the Jarvan IV, Martial Paragon over to the battlefield, who is the attacker and defender?

Your opponent is the Attacker and you're the Defender — moving Jarvan IV, Martial Paragon in afterward doesn't flip either designation.

Attacker/Defender is locked in by who first applied Contested to that battlefield (Rule 466.2.c.1), and that was your opponent's unit. By the time your unit arrives the battlefield is already Contested, so your entry doesn't apply Contested again (Rule 190.3.a.1) and nothing re-designates you. Your units simply pick up the Defender designation in the Cleanup after the move (Rule 466.2.c.3.a).

One correction on the ability: the "exhaust me and pay [A] to move a friendly unit to that battlefield" text is Exemplar of Demacia (your Legend), not Jarvan IV, Royal Heir — Royal Heir's move ability only triggers when it attacks, and it never attacked here, so no Assault bonus and no attack trigger for it.

Two things worth knowing: because the Combat opened while a Showdown was already ongoing, whoever holds Focus keeps it (Rule 466.2.c.1.b), so you still act first. And Pillaged Armory's "buff a friendly unit" trigger has to choose its unit when it's put on the chain — i.e. before the Legend's move resolves — so it can't buff the Jarvan that arrives later (same shape as FAQ #13018).