This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Secret of Kells
Old Abbot Cellach in the Distant Finale. His spirit was broken after the Vikings broke through the defenses that he'd been working on for so long and hundreds, if not thousands people died because the wall was the only thing he concentrated on, rather then supports for the stairs to the safest building (which broke under the weight of so many people, dropping them to their deaths). Plus, he had locked Brendan, his own nephew and last surviving family member, in the scriptorium as punishment for working on something other than the wall. Said scriptorium was destroyed by the Vikings and Cellach was lead to believe for years that he had caused Brendan's death.
Cellach:"How can I rest, when our greatest treasure is gone?...He was only a boy..."
Adult Brendan's face when they reunite, and Cellach tells him he has no time left. They have only just been reunited, but it won't be long before Brendan loses his uncle again.
The entire attack on the Abbey, as it results in the offscreen deaths of almost all townspeople and monks, which is overlaid by gorgeous choral music.
When Aisling seems to have been eaten/killed by Crom Cruach.
Aisling's Song. It is possibly the most beautiful song in an animated film, or in any film, period. The beauty is juxtaposed later on when the audience finds out Aisling does not get along well with Crom Cruach. Just listen to the words ... " ... you must go where I cannot ... " At least Crom Cruach was one of her own.
Abbot Cellach's reaction during the Viking attack when he realizes Brendan and Aidan are still locked in the scriptorium. Then when he regains consciousness and cries as he assumes Brendan is dead. And then of course, when Tang finds him later on, just laying there staring at the burned scriptorium, and the Abbot begs to be left alone (presumably, to be left to die like everyone else).
Brendan's tearful reaction to seeing his uncle's broken, bleeding body outside the scriptorium.