Spidey Rules 2 said:
In "Night of the Ninja" we meet Bruce's old martial arts rival. We see a young Bruce training in Japan.
In "Day of the Samurai" we meet his old sensi and of course the return of his rival.
In "Zatana" we meet....Zatana herself with some flashbacks going back to her father.
Being that its been over 24 hours since I asked my question, I may as well give the full answer.
Batman "masters" (and associates of "masters") list:
1). "Night of the Ninja": Kyudai Ken, a.k.a. The Ninja, who we see as a rival of Wayne when he trained in Japan under Sensai Yoru.
2). "Day of the Samurai": Sensai Yoru is met in the present, as well as his new prize student, Kairi Tanaga (who is kidnapped at some point by Kyodai to lure out Batman). Kyodai is able to figure out Batman's identity by his fighting style, and Yoru likely knows, too.
3). "Zatanna": In flashback, we meet Zatara the Magician, who taught Wayne the art of escaping from traps & bonds. We also meet Zatara's student/daughter, Zatanna.
4). "The Little Piggy": Zatanna again.
5). "The Balance": Zatanna again.
6). "Dead Reckoning": We meet The Master of Nanda Parbat, who Batman also apparently trained under while in the Orient, and his ghostly student/avenger, Boston Brand, a.k.a. "Deadman".
7). "Destroyer": Zatanna again.
8). & 9)."The Curse of the Kobra", Parts 1 & 2: In the future of BEYOND, Old Man Wayne once again reunites with Kairi Tanaga, who he employs to train Terry in the martial arts. In the finale, she sacrifices her life to help defeat Kobra.
I also would have accepted as an answer "Beware the Gray Ghost", as a young Wayne enjoyed the TV show GRAY GHOST as a child (as well as had "hero worship" of the star, typecast actor Simon Trent as the Gray Ghost), and after his parents were killed, this devotion likely added to Wayne's eventual donning of a caped monniker to fight crime, as well as designing the Batcave (which Trent claimed was almost a replica of the "Gray Ghost's Lair"). While Trent didn't "train" Wayne personally, his role was pivotal in creating Batman.
Since you got the most answers correct within the 24 hour limit, how about you post the next question,
Spidey Rules 2.