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Both versions of the story of Ice and Snow / Ice and Dark
The ending of episode 14, when Daisuke, alone in the darkness of his bedroom, silently pulls a veil over his painting of Risa, signifying that he's finally realized she doesn't return his feelings. Also counts as Mood Whiplash in contrast with the rest of the episode, which dealt largely with the antics of the school's new Foreign Exchange Student and super Genki Girl Mio Hio.
This troper cries every time he watches the end of this particular episode... I literally have to watch the next episode just for a change in mood.
Speaking of Mio, her whole predicament. She's a living voodoo doll who desires to be human, but in order to achieve this, she has to sacrifice Daisuke, whom she comes to genuinely care for She eventually negates the effects of the charms she gave Riku and Daisuke, sacrificing not just her chance for a human body but her doll body as well. And although for a while she appears as an annoying cockblocker for Daisuke and Riku, she actually ends upbeing greatly supportive of them in the end, telling Riku that she and Daisuke are a great couple together, in the midst of vanishing, which is a Tearjerker in universe, as both Riku and Risa are crying as it happens.
Manga volume 13 - Stage 3, vol 21: Daisuke's reaction to Satoshi telling him that his family are cursed to die young is to almost break down into tears and say they have to do something while clinging to Satoshi's arm. Satoshi is absolutely shocked - has a flashback montage of many happy moments spent together with Daisuke - and then does the closest thing to a fond smile he can do. The Ho Yay shoots back Up to Eleven for the whole chapter, but in a very, very serious and heartbreaking way for once.
Stage 4, vol 14 is also quite the Tear Jerker, and in quite the same fashion as above; if you didn't think Satoshi was a Woobie before, you sure do think so now.
The story of the Agate Links in episode 8. Back in Daisuke's grandfather's time as the Phantom Thief, he developed a friendship with an Ill Girl by the name of Menou. He wanted to give her the Agate Links as a gift, and left it at her window, but she passed away the following morning without getting the chance to see him again. However, her spirit lingered with that piece of jewelry for the next forty years, waiting for him to return just so she could thank him.