Old DM shouldn't give you much trouble. Admittedly a large magnet would probably make things a little easier, but on the whole his fight is a pretty straightforward one to ease you into the pace of NMH's boss battles. You can beat him by just using the skills you've picked up through fighting the grunts on his level, so don't worry about him too much. What his fight will teach you however, is the importance of blocking, evading, and picking your moment to attack, all of which are vital practices for every assassin battle in the game.
Just keep your finger on the Z button, unleash a combo when you get an attack window, block when he starts swinging, and you shouldn't have too much trouble at all. The only time things get tricky is towards the end of the fight when he brings in the clones of himself. You'll have to fight on a few different fronts at the same time, so get used to using the sideways and backwards rolls with the d-pad to both get out of trouble and get closer to targets quickly. Keep moving, keep the katana charged (Let go of Z and run away if you need some space to give it a good shake), and don't forget about the energy and battery boxes in the arena. You'll have him down in no time.