I couldn't finish 'em. Looks like this's gonna get complicated.
Rydia? is the final boss in Final Fantasy IV Interlude exclusive to Final Fantasy IV: The Complete Collection on the PlayStation Portable. She is fought atop the Tower of Babil. The party previously mistook her for Rydia, but she is actually a Maenad in disguise.
In the first battle with her, Rydia? is immune to damage and status ailments, and summons Shiva, Ramuh, Ifrit and then Titan to attack the party. The Eidolons each use physical blows and strong group attacks.
The battle restarts with Rydia in the party and all party members restored to full HP and MP. Rydia? opens the battle with Meteor, dealing heavy damage to the entire party, but may miss some members. After this she uses a pattern of the three third-tier elemental spells, Firaga, Blizzaga and Thundaga, cast in sequence, then Flare, Bio, and Meteor again before starting the pattern over. She always casts these spells on the entire party, even Flare.
Rydia? will counter all of Rydia's Eidolons, except for Asura, with Earthquake, and counters elemental magic from either Rydia or Palom with Blaze, Icestorm or Lightning, depending on the element. These counterattacks do significantly more damage than her normal spells, Icestorm possibly even doing as much or more damage than Meteor. Earthquake is the weakest.
After the battle resumes after Rydia joins the player's side, her Eidolons can be used safely as long as the party is not at critical health. Edge and Cecil should attack while Rydia summons Bahamut and Palom casts Bio, which will not provoke a counterattack. Porom can buff the party with Shell as all of Rydia?'s attacks are magical, and can use Haste and Berserk on Edge and Cecil to increase their damage output.
If the player is in dire need of healing and Porom is not available, Rydia can call Asura or Sylph. Rydia?'s attacks aside from Meteor and her counterattacks do not do much damage, especially if Porom is buffing the party with Shell, so as long as the player heals their party after Rydia? uses Bio and is prepared for Meteor, the battle is not difficult.