How do I defeat Baigan (first boss of FF IV Baron Castle stage)

I just went through this level with the following group:

Tyro [Lv 41] - 3* Kunai++ (10/10), 2* Mythril Helm (5/5), Power Wrist, Thunder, Curaga
Rydia [Lv 29] - 4* Light Rod (15/15), 3* Wizard Hat++ (10/10), Earring, Blizzara, Thundara
Sephiroth [Lv 42] - 5* Masamune (20/20), 4* Mythril Armor++ (15/15), Power Wrist, Double Cut
Kain [Lv 30] - 3* Kunai++ (10/10), 3* Mythril Armor+ (10/10), Power Wrist, Jump
Cloud [Lv 44] - 3* Kunai++ (10/10), 4* Mythril Helm++ (15/15), Power Wrist, Double Cut, Blizzard Strike

With this party, I was able to defeat Baigan and Cagnazzo, but unfortunately, I missed out on mastery due to Kain dying and my forgetting to hold a Blizzara for Cagnazzo (0/3 weakness to ice medals).

My strategy for Baigan was actually to kill the left arm first since that is the one that does the most damage. After burning the left arm (I used both Blizzard Strike charges I had in addition to regular attacks), I took a couple of swipes at the right arm with my heaviest hitter (Sephiroth) and then focused on the body. After doing about 14k damage, I used all of my AoE limit breaks (Sephiroth Hell's Gate, Rydia Chocobo Kick, Tyro Judgment Grimoire). This was enough to kill the body, but I must have miscalculated the right arm's HP as it self destructed and killed Kain. Even with Kain's death, I had more than enough firepower to take out Cagnazzo without any further issues.

Things I could have done better:

• Farm one more Mythril Armor and two more Mythril Helms so all four pieces I was wearing would have been 4*++ (15/15).
• Bring Slow. I forgot to bring slow to use on the right arm so it wouldn't cast buffs as frequently and possibly give me a chance to get a last shot in before it self-destructed.
• Create Shiva summon. Shiva would have been AoE ice damage on Baigan and arms and quite possibly could have made it easier to kill the body and right arm simultaneously.
• Brought Dark Cecil instead of Kain. My Dark Cecil is Lv 36 and may have been able to survive the self-destruct.

You don't mention what kind of gear or abilities you have (or other characters for that matter), so I would recommend looking at your gear first to make sure you have a good amount of record synergy gear:

• Rod++ (Rod drops in VII Mako Reactor No 1 Boss)
• Kunai++ (Kunai drops from Gargoyles in IV Fabul Castle - Room 4)
• Mythril Armor++/Mythril Helm++ (Not sure where Mythril Armor/Mythril Helm drop normally, I got mine as drops in the Friday Daily Dungeon [Armor])
• Wizard's Hat++/Black Cowl (Black Cowl is 3* and drops in V Ship Graveyard from Siren. Not sure where I got my Wizard's Hats from)

If you have Cloud, using him may help quite a bit as currently, he is the only character besides Tyro that can use spellblade skills (e.g. Thunder Strike). You can compensate for his lack of record synergy with good record synergy gear.

Slow is quite effective on Baigan, so that could help as well. Since you are using Paladin Cecil and successful casting of the status effect spells don't appear to be affected by MND (as far as I know), he would be a perfect candidate for casting Slow.

Hope this helps!