Just the name of the school would probably be fine--like, there's Karate and Tai Chi, but there's also Shorin-ryu and Goju-ryu Karate, Chen Family Tai Chi, and so on. What Dai Xin is asking isn't really "how she fights" but what the lineage is. The Japanese art of using a sword can fall under kenjutsu, iaijutsu, and a few others, and those schools have the same kind of family or traditional branches associated with them. For example, just making up a name with google translate, "Oniyuri Ittou-ryu kenjutsu" would be "Tiger Lily One Sword Style, a school of battlefield swordsmanship." That last part being because Kenjutsu is swordsmanship as used by an actual soldier, while Kendo was a later art meant to emphasize personal growth and be used more as a sport/dueling art.
Which also brings up something interesting--the kanji used for "Tiger Lily" actually mean "demon" and then the combination characters that are used for the lily flower ("hundred synthesis," probably related to having a lot of petals or something that doesn't translate literally very well). Did you intentionally tie that into how she's a "flowery" girl with a "demonic" side, cause if so that's actually really clever.