Raiko is designed to be a climactic fight, with several different stages, and she becomes more and more powerful as the fight goes on.
I built her with the intent that her performance builds up as the fight goes on, adding more and more until it builds to a crescendo.
Her Percussion action also allows her to dominate enclosed spaces, as well as set up a defensive line, or an ambush. Having a few of these set up at the start of a fight can make it much more challenging for the party.
So, to clarify on how her Ten-Part Performance works:
At the start of a fight, Raiko activates Ten-Part Performance at the beginning of her first turn.
Example 1: Raiko enters combat. At the beginning of her first turn, First Drum "Raging Temple Taiko" activates. Raiko gains 48 temporary HP. She then deals 12 thunder damage to all creatures of her choice within 60 ft. She is then free to take the rest of her turn as normal (move, take an action, bonus action etc.)
She only gains the temporary HP once.
Example 2: At the beginning of her second turn, she still has 11 of her temporary HP remaining. First Drum activates again. She does not gain temporary HP this time. She then deals 12 thunder damage to all creatures of her choice within 60 ft.
If she loses the temporary HP granted by one of her Ten-Part Performance parts, she will activate the next part at the beginning of her next turn. She does not lose any of the previous Ten-Part Performance effects.
Example 3: At the beginning of her third turn, Raiko no longer has any of the temporary HP that was granted to her from First Drum.
First, she activates First Drum. Again, she does not gain temporary HP this time. She then deals 12 thunder damage to all creatures of her choice within 60 ft.
She then activates Second Drum "Vengeful Spirit Aya-no-Tsuzumi". She gains 52 temporary HP. She then deals 8 thunder damage to all creatures of her choice within 120 ft.
In subsequent turns, she resolves all of her effects from the top of the list.
Example 4: At the beginning of her fourth turn, Raiko still has 14 of the temporary HP from Second Drum.
First Drum activates, which deals 12 thunder damage to all creatures of her choice within 60 ft.
Then, Second Drum activates, which deals 8 thunder damage to all creatures of her choice within 120 ft.
So, when she reaches Pristine Beat:
Example 5: At the beginning of her turn, Raiko has no temporary HP from Blue Lady Show, and has Pristine Beat activated.
First Drum activates. She deals 12 thunder damage to any number of creatures within 60 ft.
Second Drum activates. She deals 8 thunder damage to any number of creatures within 120 ft.
Third Drum activates. She deals 8 thunder damage to any number of creatures within 120 ft.
Death Drum activates. She forces any number of creatures within 60 ft. to make a DC 15 Strength saving throw or be knocked prone.
Fifth Drum activates. She deals 12 lightning damage to any number of creatures within 60 ft.
Sixth Drum activates. She deals 18 lightning damage to any number of creatures further than 60 ft. but within 300 ft.
Seventh Drum activates. She moves up to 30 ft. (She also has the passive effect of not provoking opportunity attacks when she moves)
Eighth Drum activates. She deals 12 lightning damage to any number of creatures within 300 ft.
Blue Lady Show activates. She causes any number of creatures within 30 ft. to make a DC 15 Charisma saving throw or become paralyzed until the beginning of her next turn.
Pristine Beat activates. She causes a creature within 30 ft. to make a DC 15 Wisdom saving throw or drop to 0 HP.
All of these abilities trigger at the start of her turn, so a DM can just work their way down from the top of the list.