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prabs: The key is to thin out the crowd. Rule of thumb is to take out those pesky projectile launching enemies first. They cause a great deal of damage and are often on a vehicle or atop a container. Your bow is an effective weapon, provided you time it right. Once they are out, it will allow you to focus on the melee ones. The smart move is to keep moving. A stationary position would render you vulnerable to be ganged up, and trust me, you wouldn't want that; not in this game at least.
Always use forward dash and jump, even for your attacks, it helps. Try and use the ultimate technique (hold down 'Triangle' to charge) as fast as possible. This is the best way to take down a chunk of crowd with some serious damage. Pick an open slot and charge up, when you see them coming, unleash it. I think the 3rd game (original version) only had one ninpo attack; Art of the True Inferno. That is again a good crowd control magic attack, but has limited usage. Each enemy has a proper pattern, study them and you'll know exactly when they are going to strike and with what attack.
If you're facing 3-4 higher tier enemies, like say the Alchemists, you need to isolate and keep attacking one of them and let the Ultimate Technique do it's job in the end. The reason why I keep stressing on the Ultimate Technique is because it has an i-frame, which means no enemy would be able to interrupt that animation till it's complete. Do note that you will be wide open for attack during the charging phase though.
All the Ninja Gaiden games are challenging. Play them when you have sufficient time. It's best not to break the flow. It can be a frustrating experience, so try not to get too involved. Take a short break, if you're dying too much. Good luck!