How do you beat chapter three boss in ninja gaiden 2?

This is a combination of understanding his attacks and the strategy you use overall...

The attacks you will experience are:

Ghost Mask: A slow moving projectile that tracks you. Use Ninpo to avoid it. This attack is rather slow, and does not handle turning very well, so the easiest way to deal with it is to run to the side of the form quickly, which causes it to slowly turn and, as it's timer runs out, it harmlessly explodes without damaging you (assuming you kept your distance).

Ram: Bites you and scrapes you along the wall. Dodge it.

Electric Attack: this kicks in whenever you get too close to it, so don't do that.

Flying Fish Attack: shoot them with arrows (they are very hard to dodge so shooting them is the best approach).

Electric Balls: Dodge them.

The head is the weak spot here, so shooting it with your arrows is the way to go -- do not try to melee him until he is upside down, which means he cannot easily defend, at which point you can attack with your melee weapon but dodge away when he twists.

You absolutely need arrows for this, so if you run out, loot more from the bodies by the tunnels.