This is actually two boss battles in one but they are considered to be one whole battle.
First battle is where you focus your attacks on Masa since he won't counterattack. Attack Mune though and they will counter with an X-Strike attack. The fight isn't too hard if you focus only on Masa.
Second battle is where it gets interesting because Masa and Mune merged together to be one monster who has powerful attacks. Important tip is that when it's storing whirlwind energy, have Crono use Wind Slash. It'll force the energy to dissipate thereby avoiding their special attack which can be devastating. Focus on using attacks like Ice Sword, Fire Sword, Napalm and Antipode Bomb and they'll go down.
I included two additional cutscenes to this and they relate to Frog and the Masamune. Watch and you'll see what I mean.
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Masa is a magical being found in 600 A.D. in Chrono Trigger. He, along with his brother Mune, is...
Masa& Mune is a magical creature found in 600 A.D. in Chrono Trigger. He is the second "boss...
Mune is a magical being found in 600 A.D. in Chrono Trigger. He, along with his brother Masa, is...