Kojūrō is a loyal retainer of Date Masamune, but also appears as a brotherly and mentor-like figure for the One-Eyed Dragon. Modeled after a typical yakuza-style gangster from the movies, his manner of speech, attitude towards his subordinates and even his secondary attack string clearly reflect this inspiration.
Kojuurou values honor and loyalty above everything else: he was ready to be executed for the “sin” of turning his sword against his master (albeit for a just cause). Kojuurou has been hinted to be stronger than his master various times (many characters’ lines when encountering him reflect this), and possibly he himself knows this; but he has unwavering faith in Masamune, despite the latter’s young age and recklessness. In the One-Eyed Dragon he sees the future leader of Japan, and is determined to bring his master’s ambition to fulfilment.