It's essential to understand that gun skills also vary in levels.
On a fixed horizontal line, with prolonged aiming and repeated shooting, even an ordinary person with no understanding of swordsmanship has a chance to slice a bullet. Correspondingly, if the gap in skill level between the swordsman and the gunman is too vast, a master swordsman can predict in advance through the gunman's aiming time and deflect the bullet.
Kazama Chihime encounters Inakawa Association thugs and can bully them with their poor gun skills. When she meets Minamoto Tamako, a professional, she can also bully her due to her need for prolonged aiming—however, when she encounters criminal police with long-term live-ammunition training, all she can do is run away.
The father and daughter meet again, without any greetings. Kazama Chihime doesn't have time to ask how he escaped the warehouse, only hearing three gunshots in succession—Kazama Tatsuya shoots first without a word.