Episode 6 shows a flashback of Gai failed to save his squad from the Leukocyte satellite. One of which is a young girl who is so injured in pain that Gai had to Mercy Kill her.
In Episode 9 we get a real doozy. We have the death of Yahiro's little brother, Jun. We're given a brief flashback to Jun's past, seeing him happily play with Yahiro as a child. And how he makes a clear point of how Lost Christmas is about to happen. You're sitting there, just waiting for the tear jerker to start as Jun explain how the Apocalypse Virus has given him the ability to see Voids, which is a textbook case of Blessed with Suck in that it lets him see the darker sides of otherwise kind and friendly people, including his beloved older brother. Then Lost Christmas Happens. and we see the memories of Yahiro swearing to protect Jun. As the virus is slowly causing him to go insane and crush his brother to death with an Endlave. And in the end, Shu is forced to kill Jun in order to protect Yahiro and end the former's suffering. Cue Heroic BSOD for Shu.
Following that we have Episode 10, where Shu briefly quits working with the Undertakers and sulks himself. Inori attempts to show a new song she made, but a frightened Shu destroys it after experiencing another flashback with a similar girl/Mana and called her a monster, Inori sadly leaves Shu's apartment afterwards.
The final scene with Shu and Inori both crying is so darn sad, but it's worse for Inori because Gai was the one who gave her a name and a world...
When you're watching Episode 12 again, when Shu calls Gai/Triton his best friend, and stops him from falling on a bridge. You know they don't have much time left together as friends. Made worse by the few seconds where it shows Gai letting go of Shu's hand at the end.
Episode 15. When Shu and Hare are severely injured, despite bleeding profusely, Hare heals Shu first. She details a fairy tale she read as a little girl, about a kind king that gave everything away to the people, how the people wound up hating him for this, and how she didn't hate him at all. She says that the kind king was her first love, and how she thinks that Shu was this kind king. And a GHQ helicopter flies over and destroys her Void, making it impossible for Hare to heal herself. Shu makes it out thanks to Hare, but Hare suddenly becomes afflicted with the Apocalypse Virus. Shu holds her as the crystal eats her alive and she vanishes into dust, right when in Shu's grip. Cue Despair Event Horizon for Shu and a subsequent Roaring Rampage of Revenge complete with Dull Eyes of Unhappiness. And you know what's really ironic? None of this probably would have happened had Souta and the other F-ranked Void users not been so brash.
Episode 17. Seeing everyone turn on Shu is absolutely heart-wrenching. Especially when you realized how favorably and idealistically everything began. Then Keido... Or Segai... Or whoever's really in charge starts pulling the strings from behind the scenes and starts screwing with everyone, causing formerly genuine Nice Guy Shu to go through his Start of Darkness and even causing his classmates, friends, and comrades who originally appreciated him as a pillar of strength in such unstable times to turn on him. And it's all topped off with a recently revived and clearly evil Gai chopping the poor kids arm off in order to steal the Void Genome. Seeing his best friends turn on him was just so awful.
Made worse by the fact that many of his friends seem to hate doing this to him. Looking at you, Souta.
In Episode 18, watching Shu look at photos of him and his 'friends' after everything that has happened is extremely heartwrenching.
Inori's speech to Shu, where she promises to always be on his side.
Inori: Who's Shu? Gai: The name of the man you loved.
That's love with a D, as in past tense.
The entire finale that is Episode 22.
When Rowan sacrifices himself to protect Daryl by pushing him into an elevator while saying "If you get another chance, be more kind to people! Deep down, I know you were a nice guy Daryl!" The expression on Daryl's face made it sadder.
Watching Gai die a second time is immensely more difficult and heart wrenching, especially when he reveals the reason why he sided with GHQ/Da'ath.
When Inori returns to herself only to revealed to have become overtaken by the virus and unable to see or feel Shu was absolutely heartbreaking. It's even followed by Shu pulling the biggest Heroic Sacrifice in the show as he absorbs the Apocalypse Virus. All of it. However, Inori's subsequent Heroic Sacrifice saves him.
The incredibly bittersweet "Release My Soul" playing during that whole scene really sells it.
Watching Ayase in tears with her head in her hands afterwards is absolutely heartwrenching.
Then there's that moment at the epilogue after the Time Skip when it looks like Shu may be settling back into a normal life, thanks to a replacement arm... and then it's revealed curing the Apocalypse Virus cost him his eyesight. And even years later, he is still mourning Inori.
In the Lost Xmas OVA, Scrooge saves the dog that Carol had grown attached to from being hit by a robot's laser. How is it a tearjerker? Because as soon as he touches it, the Apocalypse Virus crystals grow all over its body, killing it. After the battle, Carol has Dull Eyes of Unhappiness as she stares at its body.
The first opening song "My Dearest". The lyrics literally spell outeverything that will happen in the last quarter of the series, such as the fact that nearly everyone Shu knows will turn on him, Inori will be the only person left to stand by him, and that she will die saving him, hoping that she will live on in his memories.