The ORigin of Mewtwo: the deaths of Aitwo/Ambertwo and the other clones--her final moments spent comforting Mewtwo. ;____; Professor Fuji's story is also quite tragic and then, then comes the chilling final line in the movie proper.
Jirachi - Wishmaker: as soon as May starts humming her mother's lullaby and Chiisaki Mono/A Small Thing kicks in, I am gone. Utterly defeated. Such a deep and close bond with a little kid is necessary for Jirachi to wake up, but then, it can only stay awake for a week, before sleeping for a thousand years... it's such a tragic thing, there's so many sad playmates who never see Jirachi again. ;___;
The Guardians of Alto-Mare: Latios' final sightsharing with his sister and everyone breaks my heart. That glass-like tinkling of their claws as their paws separate.... ;_;
How the world looks, shrinking away, as his soul leaves the earth...
Misty's line where she softly says, as the planet shrinks away into just a distant, quiet sphere in space:
"It's our world... it's so blue."
Victini and the White/Black Hero: Reshiram/Zekrom: Ash suffocating from air deprivation, altitude sickness, and freezing to death, the light already leaving his eyes, but he's still shedding tears [that freeze before they shatter on the ground!!!], and with the last of his strength, just apologizing to Victini... it's so noble and selfless and heartbreaking.
Pokemon I Choose You!: Souji/Sorrel's backstory, which also makes how cautious he is about Pokemon and bad weather good foreshadowing.
Everyone's Story/The Power of Us: Harriet's backstory, which makes the insults and assumptions made about her by those rowdy kids in the beginning hurt that much more.