The death of Zilla, despite everything it had done and all the people who died because of him. You can't help but feel a little pity for the big guy (or girl) when he finally goes... and in his last moments he just stares at Nick with a resigned look in his eye, before shutting them for good.
The novelization adds to the tearjerkiness. For context, much of the novel is from Nick's POV, and this passage comes after the F-18s' final run:
We turned around just as Gojira's enormous head came crashing down onto the bridge. It landed directly on top of the taxicab, crushing it like a paper cup. The bridge swayed violently and the steel cables moaned, threatening to pull loose from their mighty anchors. But the bridge - or what was left of it - held, and the swaying slowly subsided.
I took a few steps back toward the creature's head, which towered above me. One of his hundred-pound eyeballs was pointed in my direction, but I don't think he saw me. The nictitating membrane was half closed and the iris had a glazed, weary look. He blinked slowly and exhaled, the breath of life slipping out of him.
I felt like rushing over to him and trying to offer him some comfort. I wanted to explain that we'd only done what we had to do. The Earth just wasn't big enough for both our species. But in the end, I just stood there. And then he was dead.
When Zilla arrived back at his nest, only to find all the babies dead. It was tragic watching him nudge that one infant, as if he were hoping his actions would help.
The death of every American and French soldier. Some of them may have been frightened but, every single one tried to do their job to the best of their abilities.