the easiest way i found was to jump above him, shoot down at him with the shotgun, then while up in the air do dante's downward slash move. After this connects simply jump again and repeat... this fills your devil trigger gauge pretty quickly so blast his ass with lightning whenever you can, then keep repeating the same strategy.
save afterwards.
When he chases you down the hall in the following area, don't be afraid to fight him. Run when he chases you down the hall, jumping over his fireballs as you go(this may take you getting killed once or twice, but the timing of how he fires the fireballs is rythmic so you don't even have to do it on reaction. Let him chase you to the end of the hall.. once there he will stop. Jump in his face and hit your devil trigger then slash away, he'll die surprisingly easily.
The benefit of this is that you get 500 red orbs for beating him. Even better is the fact that you can save and restart the mission and quickly kill him in the hall again. You can do this as much as you want before moving on. I did this for a while and ended up buying everything on the third level... definitely makes the game easier.