Remaining health - Pretty straightforward, when you finish, more health= More points, max 1000
Round use score - How long you took to finish the battle. Finish in less round =more score. It's generally between 1000-1500(less if you take more rounds to finish ). Unless you have very high stats and refinement, Jiraya and hanzo will take 3 round each to finish(or more), leading to lower score. Many strong people can kill them in 2 round, resulting in higher score.
Times died - Self explanatory. Less dead ninja = higher score. If you finish with no dead ninja, can get 500 score, which is the maximum.
Total dmg level - How much total dmg you took thoughout the battle. Less dmg taken = higher score. This isn't much important, and usually score will be between 370- 380, maybe a little more.
Those are all. As you can see, last 2 aren't that important and probably will be same for most people. First 2 however, is the main factor in doing high score, especially round use score.