The film contains intense war violence including:
One of the opening scenes where a terrorist group strikes a political building, killing many of the workers inside. People are wiped out by machine guns and explosions. In the same scene, a terrorist hails his nation before being vaporized in an explosion onscreen. Nothing truly graphic, though.
An asteroid is dropped on a colony as part of a terrorist attack, we see an entire town being vaporized but nothing graphic.
There are intense fights between Londo Bell (an anti-terrorist military force) and Neo-Zeon (a terrorist organization). The battles take up the main bulk of the action and are in the form of giant mecha. Most of the people piloting these mecha are killed by explosions during combat.
One of the only exceptions is a woman who leaves her mecha after it explodes, she is grabbed by an enemy pilot's mecha and dies when he flings her away. We barely see her body later but it's implied that the force of the throw by the giant arm may have been the cause of death.
Two men fight each other at one point with their fists, nothing graphic.
A man slaps his son, it's not graphic but the force of the slap might be startling to some viewers.