In episode 50, Aichi's anguished rant at Kai. Effects of PSY Qualia aside, he was probably keeping most of what he said bottled up inside for pretty much the entire series...
Episode 102 has quite the Tear Jerker: Aichi arrives at Leon and Kai's fight as it finishes and rushes to Kai's side, whose initially unresponsive. Kai apologizes for having not been there to fight for the sealed clans by Aichi's side, while the whole time, he sits there in tears from just listening. When Kai, Ren and Asaka begin to glow from their dismissal from Cray, Aichi clings to Kai, pleading for him not to disappear and encouraged to fight on before they disappear, which is followed by Aichi giving a Skyward ScreamSay My Name and breaking down in tears completely before Leon. Even Charlene and Jillian feel for him.
Kai's feelings of inadequacy in Link Joker. He's had them for quite some time, at least since Episode 103, some months before the third season. They slowly begin to eat away at him and it becomes increasingly difficult for him to hide his real feelings, almost opening up to Miwa, though his words are mostly lost. Their worsening correlates with Kai's declining state and culminates with Kai's conversion to Void's side, killing off part of himself while in an unstable state of mind. It gets worse as Kai's loneliness is something that the season is going to cover, leading to his Start of Darkness and in an interview, Takuya Satou reported how difficult he found it to record the episode.
Yuri's fight with Reversed Koutei in Episode 136. She's fighting an opponent she cares for a lot and who she helped rise from being basically an inept beginner to a national champion, and who is now Brainwashed and Crazy to the point of being the exact opposite of his normal self. By the end, she's screaming his name, trying to desperately bring him back to his senses, only to be cruelly defeated by Reverse Daiyusha and reduced to a mindless Reverse fighter. Made even worse if you knew Episode 137's title before, and thus know that she's in a Hopeless Boss Fight.
Gillian and Charlene getting reversed in Episode 137. The entire episode was planned brilliantly to show the audience more in depth about the relationship of Leon and the Twins, and just why the Twins are so loyal to Leon. Their interactions just melted the hearts of the audience only for Reversed Kenji and the Reversed Team SIT to thrash the party. Not only the three of them were separated to fight individually, but Leon was helpless (As he was fighting Kenji) as he sees the Twins get defeated and reversed. Gillian and Charlene were clinging to Leon's memento (a boat origami made by leaves) while trying to reach out to Leon while saying his name (In tears no less, because they had failed him) as they get engulf by the ebony flames...This is definitely one of the most heart wrenching episodes in Vanguard anime history ever.