The Elemental Archfiends are bosses in the 3D versions of Final Fantasy IV fought in the Giant of Babil. Prior to the fight, the Archfiends were revived by Zemus so they could give one last group attack upon Cecil Harvey and his party.
The bosses are fought one after the other. The fiends are fought in the same order they were first encountered; Scarmiglione, Cagnazzo, Barbariccia, and Rubicante.
Scarmiglione is weak to Fire and uses debuffs and Cursed Elegy as a counter.
Cagnazzo is weak to Lightning.
Barbariccia is immune to physical attacks due to the absence of Kain and his Jump ability, but magical attacks are capable of harming her. Barbariccia does not counter attacks as much, but she does attack more frequently than before. Though it is not mentioned in the bestiary, Holy magic is incredibly effective against her.
Against Barbariccia Edge and Cecil have little to contribute offensively, so Rydia and Fusoya should focus on dealing out damage while Cecil and Rosa keep everyone's health up. Fusoya can cast Holy or Rydia can summon Dragon. If Rosa is a high enough level, she can Dualcast Holy dealing approximately 19998 damage.
When up against Rubicante, the player can use the same strategies as in the first encounter, except this time Fusoya replaces Kain—he works well as a second Black Mage (casting Blizzara and Blizzaga, for example) or as an additional White Mage if needed. If the player has completed the sidequest in the Feymarch and have access to Leviathan they should summon him here, as it is particularly devastating against Rubicante and can easily cause 9,999 HP of damage.
An alternate strategy is to cast Haste on Rydia, then use Shiva or Leviathan when Rubicante opens his cloak (more preferable with Shiva as she is faster), then use Steal with Edge. After around four turns of this, Rubicante should fall. Since Rubicante should not be able to use Inferno when in his cloak, he will only be able to physically attack. Rosa can either revive characters killed with Rubicante's physical attack, or cast a Fire spell on Rubicante.