This is an analysis of all Ryuki moments in Digimon Tamers based on the main characteristics of Rika and Ryo's relationship that I wrote about here. I decided to leave the names in the original here because I will mostly be quoting from the Japanese version of Tamers.
I watched Digimon Tamers subtitled by the wonderful WildBunch.
Ruki, Hirokazu and Kenta are transported to a strange part of the Digiworld. First thing they notice is a broken clock and Ruki fixes it before Hagurumon and Clockmon stop her. The ground starts shaking and an evil Megadramon appears. The Digimon is in its Ultimate level and is too strong for Kyubimon. Suddenly, Cyberdramon appears and saves them from the badguy but doesn't stop fighting it even when Megadramon is already incapable to fight back and the fight is hard to watch. Ryo appears and asks Cyberdramon to stop fighting but the Digimon doesn't listen. Ruki's shocked when she sees Ryo, recognizing him probably as her number one rival. When Ryo then stops Cyberdramon with the D-Power whip, she approaches him with an unpleasant look on her face.
However, Ryo shocks her with the sudden change of his mood, when he turns around with a pleasant smile, his frustration with Cyberdramon's behaviour completely gone. Ruki is speechless for a moment (she even blinks twice in confusion) and Ryo grabs her hand, shakes it and introduces himself. She looks confused but comes back to herself a moment later and when Ryo warns them about the dangerous Digimon she snaps at him (while Kyubimon politely nods to Ryo's warning).
Ryo basically lectures them on the dangerous of the DigiWorld and even does this teacher-like movement with his hand. No wonder Ruki's mad. She just met her biggest rival and it was in the worst possible moment. She was powerless against an Ultimate Digimon, when he suddenly came to save them and then he talked to them as if he had some kind of authority of a more experienced Tamer. Ryo probably noticed he was older than the three of them and acted like a normal 14-year-old would when meeting someone 4 years younger. Oh my, they're all so young.
Ryo then fixes Hagurumon and the clock and has a very corny conversation with the two Digimon but okay, he's just being really nice - and really annoying to someone:
Hirokazu and Kenta then recognize Ryo as the Legendary Tamer Akiyama Ryo but Ruki doesn't bat an eye at this discovery, since she had to recognize him straight away. Ryo's pretty humble about his fame and looks a bit embarassed by Hirokazu and Kenta's excitement.
They're sitting by the fire later and Ryo learns about the rest of their group and their reason for coming to the DigiWorld. He tells them he's been in the DigiWorld for the last 10 months because of Cyberdramon. Ruki can't keep her frustration to herself anymore and gets into a fight with Hirokazu, who's just being a giant ass.
Ruki's annoyance escalates into anger when Hirokazu tells her Ryo's better at Digimon TCG than her and then Ryo doesn't even remember ever battling her. She denies remembering him but it's clear she's just too stubborn and angry to admit it (how would the Digimon Queen not remember her only worthy opponent?). Ryo then scolds her again for being rude but doesn't resent her harsh words, he just chooses to ignore them. And makes her mad even more.
Ryo then invites them to leave this part of the DigiWorld with him because he knows the way. Hirokazu is super excited to go but Kenta is more reserved and asks Ruki what she feels about that. Ruki's cooled down and doesn't yell anymore but is still so upset with the whole situation that she decides to ditch them and find the way out on her own (RUKI: "How do you know we can't get out by going up? I think we can."). Ryo tries to warn her about the place but she doesn't want to listen to him. SHe and Kyubimon go their separate way. Ryo's frustrated by her, worried and a bit annoyed even (RYO: "What's with her?").
Takato and the others meet Ryo, Hirokazu and Kenta in a black-n-white part of the DigiWorld. Takato and Jian recognize Ryo as the Tamer that disappeared to a DigiWorld after winning a tournament. When they see Ruki's not with them anymore, Takato guesses that it must had been Hirokazu's fault but Ryo's the one feeling responsible for it. He still feels bad about it later when Juri mentions Ruki again.
Meanwhile, Ruki and Renamon are still walking around the clock-world and searching for the exit. Renamon expresses doubts about Ruki's decision to not follow Ryo but Ruki can't even hear his name:
Renamon doesn't understand why she dislikes him so much but Ruki doesn't want to talk about it.
The rest of the group stays with Ryo during the night. He shows them the way to the desert-part of the DigiWorld and just as they get there, they see Majiramon and Makuramon. Cyberdramon gets agressive again and wants to fight the dragon deva. He defeats him but gets really impatient and wants to continue fighting. Ryo knows it's time to leave the Tamers and search for new opponents until Cyberdramon calms down.
(Ryo then turns around one last time:)
RYO (playfully): Ah, by the way... if you see Ruki, tell her I said hi!
TAKATO (confused): Okay!
He then jumps on Cyberdramon and leaves the rest looking confused. He asks Takato to say hi to Ruki to tease her. He must know she won't be too happy about it. Aaand this is the first sign of his affection for her.
Ruki, Renamon and Culumon finally reunite with the rest of the group. Now that they're all together, it's time they returned home to the Real World. Nobody knows how to do that and Hirokazu suggests they ask Ryo for help:
Ruki can't stop herself to complain about Ryo but doesn't want to admit how much he's bothering her. At this point she'd still rather see them try to find a solution by themselves and not ask that guy for any help (even if it made it easier for them).
Ryo and Cyberdramon join the rest of the group at the top of the chasm where Culumon is being captured. The two go there because the D-Reaper seems to be the enemy they were looking for. The group is happy to see them and Ryo tries to talk to Ruki but she's not ready to get over their rivalry and has nothing nice to say to him.
Zhuqiaomon returns from the chasm, injured from the D-Reaper. Tamers know they're running out of time to save Culumon and Ruki decides to go down the cliff to explore the area. Of course she does so without consulting anyone and while the group is more or else used to her doing that, Ryo tries to change her mind because he thinks it's to dangerous (RYO: "Come back, Ruki! That's crazy!"). And of course she ignores everything he says. Renamon joins her and Ryo decides to follow them too, when Ruki slips and almost falls but it caught by Renamon.
They go down the chasm and Ruki finally gets to Culumon. After the short moment of reunion a D-Reaper bubble almost touches them but Renamon is there to pull them away. Ruki's backpack is however erased by it. Ryo pulls them into a cave and saves them from a second bubble. He accuses Ruki of being too reckless but she points out how he's no less reckless than her for going after her.
Then she's actually ready to discuss an escape plan with him. They both know how to act in a dangerous situation and Ruki puts her differences with Ryo aside.
Ryo has an idea that could buy them some time and helps Cyberdramon to trap the bubbles (oh, he uses another Device card to do it, I just noticed). The idea works and Ruki agrees with Ryo it's time to get out - she even nods to him. They have to hurry though before the bubbles explode under the pressure of the barrier the two had created.
However, the bubbles come through and Ruki knows they'll hurt them and their friends if they don't do anything about it.
Ryo goes up to her and she gives him Culumon. He takes the Digimon but holds her hands too in the process, aaw. ♡ When she tells him to take care of Culumon and goes slides down towards the bubble he screams after her to return, worried. The rest of the group hears him screaming her name.
He screams her name one last time when she jumps into the bubbles with Renamon to evolve to Sakuyamon.
Sakuyamon is strong enough to capture the bubbles long enough for them all to get away from the chasm. Ryo is amazed by Ruki and also tells her so. Ruki smiles to that.
They all return to a solid ground before the D-Reaper strikes again.
Tamers finally hear from Yamaki, who tells them an ark will come for them in 40 minutes and get them back to the Real World. They have return to the desert part of the DigiWorld and the two Sovereigns tell them to go and leave the D-Reaper to them. They now have 30 minutes before the ark comes, when Renamon asks Ruki to go save Impmon with her. She agrees and they tell the rest that they're leaving.
Ryo now understands that Ruki can take care of herself regardless of how reckless her decisions seem to be. He doesn't oppose their decission and just tells them to be back in time. She winks back to him and puts her thumb up in agreement. She's definitely stopped to blindly dislike him. And in German version she even says: "Rely on that, pretty boy!". 😏
The ark appears on time but the connection isn't stable and they have to go immediately. However, Ruki and Renamon aren't back yet. Takato is waiting for them outside while the rest had already boarded the ark and Terriermon suggests to go after Ruki. Ryo jumps in very heroically and goes search for her with Cyberdramon. I guess the writers wanted to show Ryo's hero-boy side in this scene, why else would he jump in like this in the moment of Jian's hesitation. And maybe Ruki actually appreciated him coming after her, considering how nice she is to him later in the ark.
Anyway, they all board the ark on time because Guilmon manages to stop it from leaving. Ruki sits next to (D-Reaper) Juri and pets her puppet when Ryo engages her in a conversation.
Ruki actually pokes Ryo's cheek and jokes with him. That's such a huge step from how she used to communicate with him and it's quite out of her character. Of course they'd just successfully boarded an ark that will finally take them home, their mission was successful (although they'd lost Leomon and Juri was a mess) and I can just feel how relieved they must feel. This would definitely affect her behaviour but it's clear that ever since she and Renamon evolved to Sakuyamon, she'd been treating Ryo differently. There's also the look that Jian gives them when they both start laughing that I interpreted as him being happy Ruki's opened herself to other people and overcome her grudge.
Ryo returns from Kyushu in Cyberdramon's Mega level, Justimon. He mysteriously appears in the end of episode 45 but introduces himself in the beginning of episode 46. I wrote this elsewhere on the page also but this appearance is the most outrageous scene in the entire series, I swear! There's Ryo&Cyberdramon's Best Tamer song playing in the background (which is one of my favourite Best Tamer songs), the sun is shining on him, making him look like a ray of light in an otherwise dark (very cloudy) moment and then he dares to jump off the building and demonstrate his attack (named Justice Kick, which just makes everything worse). Ruki agrees with everything I just wrote. She and Hirokazu are the only ones reacting to the newcomer.
Although Ruki stopped perceiving Ryo as a rival, she's still annoyed by his "perfect sparkling aura". The perfect hero-boy's Mega level is the embodiment of justice, oh my.. Anywho, Ruki continues to refer to Ryo and his personality as "refreshing" (although not always annoyed). The adjective even made it to the title of this episode!
Jian finally sends a message to Ruki and Takato, letting them know the time for their final battle has come. They meet back in Shinjuku and just as Jian explains about the Red Card, Justimon joins them.
They're happy to see him and Ruki is nice to him too, proving she can normal around him when he's being normal and not doing anything outrageous. She's a bit more sarcastic (or just surprised to see him?) in German version where she tells him they completely forgot about him and there's a whole love-triangle-drama in the American dubs.
After slashing the Red Card they can finally enter the D-Reaper Zone in ther Mega levels. They have a little bonding moment before the final battle really begins and Ryo pretty explicitly shows his affection for Ruki. And touches a nerve!
While Dukemon goes to save Juri, the rest are trying to defeat the enormous Reaper. Justimon comes to the conclusion that the D-Reaper agent is too strong to be defeated by a single Digimon and that their only chance is to combine their powers. He asks Sakuyamon for help.
Ruki refuses to do it at first and her initial concern is Ryo's well-being. He asks her to do it regardless what it could do to him because he believes it's their only chance at winning. Ruki's eyes tear up when she decides to go through it and she tells him he's the most reckless one (of the two?). He sees it as a compliment (was he giving her compliments all the times he accused her of being reckless?). This is the first serious conversation they have that's above any sarcasm or teasing (Ryo's reply is playful a bit I guess) and it even makes Ruki cry. She proves her character growth by giving her rival all her powers and letting him be the one to defeat the enemy. I wouldn't say Ryo does this to impress her, I think he genuinely thinks it's the only shot they have left, no matter how reckless it is. They both proved to be reckless sometimes because they always take matters into their own hands, which makes them a lot alike.
Justimon successfully (and painfully) absorbs all Sakuyamon's power.
He then successfully cuts the Reaper in half but the agent glues itself back together, making the whole plan useless (and the scene unnecessary?). It's the four Sovereigns who defeat it in the end.