Yes, Space Captain Harlock is a little uneven. At times it's laughably melodramatic and at other times it's profoundly sublime.
For context: the lady with the gun is an assassin from an invading army of space aliens (their men aren't permitted to be in combat). Professor Drake is the only man left alive who believes an invasion coming, the rest were assassinated. That box he drops is some sort of storage device with proof of the invasion and the guy running up the stairs is his son.