Naruto could use his improved taijutsu skills. He might close in on Gato quickly and land a series of powerful punches and kicks that Gato can't defend against. Since Naruto is quite fast and has good reflexes, he could easily overwhelm Gato in close - combat.
It could be that Naruto has some sort of intel about Adaly White's weakness. He uses this knowledge to his advantage in the Gato base. He might first disable any guards or traps around Adaly White and then use his chakra - enhanced strength to land a fatal blow.
In a 'Naruto kills Gato' fanfiction, the plot could start with Gato's continued oppression in the Land of Waves. Naruto, having witnessed the suffering of the villagers, decides he's had enough. He uses his Shadow Clone Jutsu to surround Gato and his men. With a swift combination of Rasengan and his ninja skills, he takes Gato by surprise and defeats him, thus liberating the Land of Waves in a more direct and violent way compared to the original story.
Well, one possible plot could be that Gato has some new evil plan in the Land of Waves. Naruto, having grown stronger, decides he can't let Gato harm the innocent people there anymore. He uses his new jutsu and his quick thinking to outwit Gato's men first. Then, in a final showdown, Naruto unleashes a powerful Rasengan, directly hitting Gato and killing him, thus saving the Land of Waves from Gato's tyranny.
The 'choes' could be represented as the memories or legacies of the characters. For instance, the echoes of Naruto's determination to become Hokage could inspire some Akame ga Kill characters to strive for a better world in a different way. Or the echoes of Akame's past assassinations could haunt the Naruto characters, making them more aware of the darkness that can exist in a world.
One possible motivation could be power. Orochimaru is always seeking more power, and Naruto has the power of the Nine - Tails. He might think that by killing Naruto and somehow harnessing the Nine - Tails' power, he could become even stronger.
Perhaps Naruto discovers a forbidden music jutsu. This jutsu allows him to turn music into a physical force. When he sings or plays an instrument, the music creates sharp blades of sound that can cut through his enemies. He might also be able to use the rhythm of the music to disrupt the enemy's chakra flow, causing them to collapse and die.
The story could also take a turn where Tayuya actually has a change of heart before she even tries to attack Naruto. She could learn something about Naruto that makes her realize he's not the enemy she thought he was. For example, she might find out about his difficult past and how he overcame it, and this could make her reluctant to carry out the kill order.
To write their interactions realistically, first understand their personalities. Naruto is outgoing and determined, while the Mizukage is likely more reserved and has the responsibility of leading her village. So, when they meet, Naruto might be the one to initiate conversation in a friendly, if not a bit over - enthusiastic way. The Mizukage would be cautious at first. For example, if Naruto offers help, the Mizukage would consider the implications for her village before accepting. Their interactions should also be influenced by their respective village's history and politics. For instance, past conflicts between the Leaf and Mist villages would add an undercurrent of tension to their early encounters.
The villagers of the Land of Waves would surely support Naruto. They have suffered a great deal under Gato's rule, so they would see Naruto as their savior. Also, Sasuke might support Naruto. Even though they have their differences, Sasuke would recognize the need to stop someone as evil as Gato.
One way could be that Naruto uses his Sage Mode. In this mode, his senses and power are enhanced. He could sense the Night King's weak points and then use a super - charged Rasengan to strike at the heart of the Night King, which might be his most vulnerable part. Since Naruto can also gather natural energy, he could disrupt the dark magic that sustains the Night King.