This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / From Fake Dreams
Chapter 23, where the letter Kiritsugu left behind for Saber was revealed, you can clearly see the grief and desperation that has gripped the man, to the point where he was actually putting his faith in a Heroic Spirit, an entity which he had despised for the better portion of his life due to them (from his point of view) being no better than common murderers.
Save them Saber. Please save my children. I have bet everything on you and Shirou to make things right where I have failed, where I have gambled everything on a lie and gained nothing but destruction. Every other attempt I have had at trying to make someone close to me happy and live has ended only in death, violence, and sending them on the path of ruin.
Please give me a reason to believe that there is worth in heroes one last time.
The 'blink and you'll miss it' mention about some of Archer's previous summons as a Counter Guardian. He's had to kill Sakuramultiple times.
Chapter 34 has Rin pretty much start to break down after Luvia and Princess!Medea help her realize that Archer's attitude, different Reality Marble, and lack of a recorded Legend all point to him being a Counter Guardian.
What makes it worse, is that because she's unaware that this Shirou is not her timeline's Shirou, it makes her believe that all her efforts to curb Shirou's distortion were for naught.
The chapters afterward are not any better almost breaking her time and again.
Chapter 43: Ilya's maids die because of Caster's dragon fang warriors.
Chapter 45 finally drives home the difference between Shirou and Archer: if Archer inherited Kiritsugu's ideals, FFD!Shirou inherited his regrets. This means Archer and Shirou are so different on a fundamental level, they will never be able to understand or accept each other, even more so than in canon.
Taiga (who may have more of an active role in canon) also actually had one when reminiscing about Kiritsugu with Shirou.
Kiritsugu's scared mannerisms in regards to his son once he saw the Archer route. That left poor Shirou with some emotional trauma that came back with a vengeance when he saw JUST what Kiritsugu wanted him to avoid, when he met Archer.
This also means Archer's VERY EXISTENCE causes untold anguish to Shirou, sending him in a borderline Unstoppable Rage in chapter 46, where Rin has to blackmail him with his kitchen to stop him from trying to kill Archer. "He will deny me" all right.
Chapter 46, when Shirou hands over to Luvia a complete file about himself and every single thing that could get him imprisoned/killed/worse. Princess!Caster comments he is genuine and that his heart is in the right place, but he goes about it in such a clumsy way, that it comes across as very sad. Luvia herself is quite moved by how selfless an idiot Shirou is. It's even more tragic when you realize Shirou had been toying with the idea of disappearing for a few months, and he seems to just brush it off as part of his plan.
Chapter 47 has Illya interacting with Archer, and the revelation of just how worn down the countless summons and Grail Wars have left him. She begs him to hold on to what few memories he has left when the War is over, to not lose more of himself to the haze of constant killing and death, and he can't even promise that much anymore.
Chapter 48 has Witch!Caster finally getting her just desserts. Still, given how pathetically she gets owned, and with all the crap she has been forced to go through in life and after, one can't help but feel a very little bit sorry for her. She loses absolutely everything, and then as she was about to cause everything to blow up as a last ditch attempt, she gets shot in the back by Assassin, ultimately coming off as a wretched being who was until the end played by everyone, and who had to be put down for the greater good. On a meta level this cements how ruthless Shirou can be, and how far he has diverged from his Canon self, who would have striven to save everyone.
Chapter 49 has a moment with Illya and Assassin that is both this and Heartwarming. The reason why it is tear-jerking is because of all the pent up feelings on both sides, and the fact that most likely Assassin expects to disappear, given that his role is over. It is also extremely gut-wrenching to hear Illya acknowledge she is not up to the task of caring for Shirou alone.