Kanzuki-Ryu Kakutojutsu, also known as Kanzuki Style Martial Arts, refers to an original martial art style created by Karin.
Karin has a wide array of strikes, throws and potent reversals, and she prides herself on being able to handle any opponent she faces. She prefers to keep her opponents guessing by varying the speed of her attacks, and also makes them second-guess their own choice of moves for fear of her powerful counterattacks.
She is well versed in various forms of Bushido, military arts, and "combative sports". This was probably mistranslated from a term that meant "combat sports", which includes various events (e.g. Japanese Pro Wrestling and Mixed Martial Arts groups). The sum of all her accomplishments in the field of martial arts is equivalent to 100 dan and 8 kyu (the Japanese ranking system for martial arts, among other things).