Before the White Death dispatches Ladybug, the two henchmen who've been ordered to open the briefcase Ladybug was supposed to steal finally complete their task. However, earlier in the film, Prince got Kimura to crack the case's code and rigged it to blow when it was opened again. So as soon as the White Death's goons lift the case's lid, it explodes, blowing Ladybug back onto the unmoving train, followed by the White Death and several henchmen. This buys Ladybug enough time to escape the White Death's clutches.
At this point, the White Death is distracted by another issue — Prince, whose every move has been about assassinating the crime lord. When the White Death enters the train, he's confronted by Prince, and she makes it clear that the reason she's so determined to take him out is that he's her father. Yes, Prince has threatened Kimura's young son's life twice, manipulated, killed, and rigged a suitcase with explosives because she's a sociopath with Daddy issues.
Prince's grievance seems to be that the White Death never paid attention to her because she's a girl. While most people would seek therapy to cope with the rejection, Prince has gone another way, and even as she waves a gun in her father's face, she's still pursuing her endgame. The White Death is known for killing anyone who crosses him with the weapon they threatened him with, and Prince expects that's exactly what he'll do to her. She even hands him the gun. However, earlier in the movie, in anticipation of this exact moment, Prince rigs her gun to backfire, killing whoever pulls the trigger.
Despite her tears, Prince is actually anticipating violently besting her father. Unfortunately, while the White Death accepts the gun, he declines to kill Prince — leaving her feeling slighted once again.
