This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / Heaven's Lost Property
After the ending sequence of episode eight, Ikaros shows that she's Not So Stoic and starts crying.
Nymph's backstory, as revealed in episode 10. For her entire life she was physically and emotionally abused by Minos for his own sick amusement. She was forced by Minos to kill her pet bird, who was pretty much her only friend, as an alternative to being killed herself. Then, during the credits for episode 12, a montage of pictures from Nymph's memories shows that she first met the bird after one of Minos' beatings. It was the only thing that comforted her in her shitty life, making it that much worse when she was forced to kill it.
Chaos being UTTERLY shattered to pieces in chapter 47.
Harpy Older mentally calling out to the Master when she's drowning.
Chapter 66. The Harpies decide to go against Minos' orders to kill Tomoki and destroy Ikaros, and their collars go off, which ends up in their destruction. Everyone is highly distraught because they couldn't do anything to stop them, and the chapter ends with Tomoki gazing at the sky... showing signs of Unstoppable Ragefor the first time in the entire series.
Made even worse by the fact that Minos himself was about to tell them to stop and looked utterly crushed afterwards. Saddest part of the whole series to me.
Ever wondered why Sugata gets so upset when his family or home is brought up? Chapter 67 reveals that it was because he was often ignored by his parents. When he witnesses Tomoyo comforting Tomoki after the latter is bummed about the Harpies' death he decides to pay a visit to his home... and we see his mother seemingly running to embrace her returning son... only for his mother to run right past him and hug her younger child instead... and no one seems to even acknowledge Sugata's presence there... to the point of calling him a “total stranger” when his little brother asked who he was. It's quite heartwrenching to see someone face all this...
Chapter 70's entirety... After the Hiyori-centric chapter 69 ends with Chaos appearing in Hiyori's house, half the chapter is Hiyori running away from Chaos in horror, to no avail. After having her left wing destroyed and Demeter sliced into bits, Hiyori, by being stabbed by Chaos' wings, could feel just how emotionally broken she was. Then after Chaos seems to calm down and Hiyori hugs her, everything seems like it's gonna be alright... until Hiyori stabs herself with Chaos' wings so she can understand how wrong hurting people is, thus killing her AGAIN... To top it all off, we are afterwards shown all of Hiyori's dreams and how much she wanted to have a happy life together with Tomoki... All of which she willingly sacrificed to help Chaos. Chaos bursts into tears, reveals herself as an angeloid to Tomoki... And then Nymph finds Hiyori's broken body... Instantly crying Berserker Tears... Damnit Suu...
Even worse, the previous chapter also centered on Nymph suffering from loneliness, thinking that every time she makes friends, they leave her one way or the other, like the bird Minos ordered her to crush, and in the end of the chapter, after Hiyori gets flustered and Nymph calms her down, Hiyori asks Nymph if they could be friends. Then... She finds her new friend destroyed by Chaos, making her yet another friend that leaves her. Again, Damnit Suu...
Chapter 71. Tomoki gets killed trying to stop Chaos and Nymph from fighting and effectively pushes Ikaros, Nymph, Astraea, Sohara, and Chaos full force into the Despair Event Horizon... with Chaos being emotionally shattered, leading her to run away and kidnap Sugata. Once more, DAMNIT SUU!
Chapter 72. After a very brief comedic moment where Oregano shows up to heal Tomoki, it turns out that Chaos is bringing Sugata to Synapse to remake the world, similar to how Tomoki remade the world back in Chapter 2.. As a result of that, Sohara disappears crying, not even able to to tell Tomoki that she loves him. It just gets worse and worse.
Chapter 75 just ups the ante. Both Chaos AND Delta are killed off!
Chapter 76 goes even further. Nymph seemingly betrays Tomoki and the others by agreeing to be Minos's angeloid again...but it turns out she planned to take him and the other Melan Angeloids all at once by blowing herself up. Also as a reference to the mythological character, Ikaros's wings burn up while she and Tomoki are heading to the Synapse. It looks like nobody is going to survive at the end.
Not to mention Mikako tenderly holding Sugata's body under the trees of Synapse. Could double as a Crowning Moment of Heartwarming, if you can take the time to stop crying and see how peaceful they look.