One thing I would really love about Aqua training Kairi is how they can both relate to losing someone they love and trying to get them back.
Maybe a scene that goes something along the lines of this?
Kairi (determined, keyblade out): Fight me, Master Aqua.
Aqua (surprised): Kairi? What's wrong?
Kairi: I need to get stronger. So, fight me!
Aqua (concerned): I- I don't understand. Why-
Kairi (upset): I need to rescue Sora! I need to help Riku! There's so much I need to-
Aqua: Slow down, Kairi. It's okay, just-
Kairi (starting to cry): Aqua, I just- I don't know what to do. When Sora went missing, Rik- They told me to- to go and sleep!
Aqua (calm): Shhhh, calm down and breathe. It's alright.
Kairi (sobbing): What does sleeping do? How am I supposed to help Sora and Riku by sleeping?!
Aqua puts her arms around Kairi and hugs her tight. Kairi buries her head in Aqua's stomach, sobbing.
Kairi: I'm just so... sick of all of this. It's so stupid. It's been a whole year and nothing's happened. And Riku-
Kairi takes a deep breath.
Kairi (calming down): I'm not sure if I can trust Riku anymore.
Aqua (anxiously): Kairi, why?
Kairi: He's just- What has he been doing? I mean, at least I was asleep, getting my heart studied but Riku... He didn't find anything suspicious that he'd been having the same dream on repeat for a year. He didn't help out in trying to find Sora, unlike everybody else. Instead he just- plays video games!
Aqua: Kairi... This has been hard on Riku. It's not his fault.
Kairi (chuckling sadly): I guess... That I'm not much better, am I? Just sleeping for an entire year.
Aqua: Kairi! Don't say that about yoursel-
Kairi: Aqua, it's- it's true. I... haven't been doing anything. I- Everyone knows it's my fault. If I hadn't been so stupid as to get caught then- Then Sora might still be here! If it hadn't been for me then Riku would be happy and-
Kairi curls up.
Kairi: And he wouldn't hate me.
Aqua grabs Kairi's hands and looks her in her eyes.
Aqua: None of this is your fault, and Riku doesn't blame you for what happened. You're his friend.
Kairi (pulling away): That's not true, Aqua. This is all my fault. I'm- I'm not strong like you.
Aqua (softly): Kairi... I'm not strong. Not at all.
Kairi (eyes widening): What do you mean? You're the strongest, most brave person I know. Well, next to Sora and Riku, of course.
Aqua (smiling, blushing): But I'm far from strong. I couldn't do anything in the Realm of Darkness. I was always longing for Terra and Ven. They're what kept me from giving up.
Aqua pauses.
Aqua (sighing): I remember how lonely it was without them. I... missed them so much.
Kairi stands up.
Kairi (hurt): Then you should understand the most!
Aqua: Huh?
Kairi: You should understand what it means to lose someone you love and the feeling that you want them back! Sora keeps me from giving up.
Aqua (sighing, closing her eyes): Kairi, I'm not going to fight you. That isn't how you get stronger. I'm going to help you train-
Kairi: No! I need to beat you.
Aqua (surprised): What? Why?! We shouldn't be fighting amongst ourselves, Kai-
Kairi: Master Aqua, fight me.
Kairi summons her keyblade and gets into a fighting stance.
Kairi: I need to know if I'm worthy.