The fight starts with just Muraga, who is quite a distance away from the team's initial location. They use Dark magic and slash attacks. All parts of Muraga can deal counter attack damage, but only the main body has the counter attack damage that can inflict disable.
On the first turn, Muraga will use a 3 hit barrier against phys and magic attacks. Defeating the main body will defeat the other parts as well. When the main body's HP gets low, the other body parts can heal him. With every defeated body part, the main body will lose some of its buffs like DEF, SPR, and Elemental Resists, but will also gain some buffs like regen or AGI.
4 arcane serpents will show up when the main body's HP is lower than 70%. 2 on each side of the map will appear.
Guide
Players with strong accounts might not have much trouble with the fight, but it can be a struggle for a lot of players not ready for this.
It can really help with the fight if you have at least one of these things:
A barrier breaking area attack.
Multihit area attack.
Strong Light damage dealers.
A tank is definitely necessary too, but many units can fill that slot, so it's not as restrictive. Charlotte might be the best unit to tank the fight since she has DEF and SPR debuff resistance, as well as good magic resistance skills. Otherwise, you can use any unit with a spellblade job and give it some slash resist.
Barrier Breakers
Many damage dealers have barrier breaking attacks, but there are certain units like Helena (Black-Robed Witch), Duane, Kilphe (Summer) have skills that break barriers in an area. Every time a barrier is down, the main body will use the barrier skill again. This can help prevent some damage taken, but can also be taken advantage of if your barrier breakers get the first turn right after the body.
If dispel also works CMIIW, then you can also use units with sniper job like Corwell, Niv Lu, or Viktora (Winter) for their area dispel attack.
Multi hit area attacks
If you don't have barrier breakers, multi hit attacks like from Cloud, or Starlight Elena can also work. Ideally, you want the multi hit attackers to be the same attack type as your other damage dealers as well. Elena and/or Cloud are good options because slash is somewhat common, so you can have someone like Warrior of Light be a finisher. Elsirelle is also a good finisher, but without an EX job, her max damage cap is only 9,999. She has maiming slash to help reduce healing received for muraga though.
Evasion
Evasion has been known to work quite well against Muraga. If you have invested in evasion setups(Shiva VC, Sages Hat, etc), you can make them your designated tank. You might have to use long range damage dealers to avoid others getting hit though since there is no dedicated tank with some hate increasing skills other than maybe Zazan the Unkillable.
If you can afford it, Vow of Love can be equipped on your main evasion unit to help with hate. If your units don't have high evasion, you can reduce enemy's accuracy with someone like Tifa.
Helena & Duane
You don't have to take advantage of elemental advantage and go with Light units. Though, going with Dark element mostly works because Helena and Duane are very strong. Not only do both of them have barrier breaking area attacks, but they can reduce enemy's resistances, allowing your other damage dealers to hit pretty hard even if Muraga still has the barrier. If you happen to have these 2 units as a combo, you might be able to fully auto the fight.
Supports
Units with Green Mage sub job can use Imperil to help increase damage, even better if those units can also heal. Ayaka is a pretty good unit to bring since she also has Esuna to cure disable, while Yuna is able to provide some damage to the enemy as well.
Frederika's TMR can also help prevent the disable, but not cure it. You can put this on any unit and cast it in battle early on for your main tank.