The death of the unnamed wolfman. The reveal is difficult enough, but the way it's handled is excruciatingly brutal.
Spoilers ahead: Handled is a very good term, since he died in his full wolf form, the guys tasked with picking the body up simply throw it into a bag and toss it into a trash compactor. The fact that Hana has to watch all this and canīt even properly bury him is heart crushing.
When Ame almost drowned trying to catch a bird, very much in the same way his father died. The sight of Hana hugging him so closely and crying, as if he was going to vanish if she ever let him go, is heartrending.
Ame and Yuki arguing over their choices to live as either human or wolf, devolving into them fighting each other in their wolf forms. Seeing Yuki scratched up and holding herself as she cries in the bath is just... ugh.
Ame's departure at the end of the film starts this way, with Hana desperately begging her son to come back.
Hana: But I still haven't done a single thing for you...
What makes this even more heartbreaking is Ame's response to that line. By this point in the film, he's been established as maturing into being a fairly aloof and stoic character. His response to that line is one of being near to tears.
He's become so lupine that he won't even speak. He just looks back at his mother regretfully, then runs away into the forest, presumably with no intention to ever return. Then he runs to the top of a mountain and just howls.
"The magic words didn't work no matter how many times I tried." Yuki completely breaks down in tears in Hana's car after she had accidentally hurt Sohei. She can't hold back her sobbing AT ALL, and it cuts straight to the heart.
"Okaasan no Uta" (Song of Mother). Dear lord.
I can do it for you. Is there already nothing left?
Someday, when you start your journey, I'll be sure to smile and see you off.
But I will be a bit lonely.
A Fridge Horror tear jerker. At the beginning of the day of the huge rainstorm, there's brief interaction between Yuki & Ame before Yuki goes to school. Ame asks Yuki to stay home that day and keep their mom company, Yuki declines, and then she leaves. This is obviously heart-wrenching, first of all, because Ame has probably decided by this point that he's gonna run away, and also because he knows it's going to storm badly. He doesn't want Hana to be alone and have to deal with all of that. This in itself is both a Tear Jerker and a Crowning Moment Of Heart Warming, but it gets even sadder with the Fridge Horror. That small, seemingly insignificant interaction between the two siblings is the last time they ever see each other. Yuki and Ame never got to say goodbye...