I was a victim in a hit-run case and the hitter run from the accident site, but I've noted his car number. Is it possible to file a case against him? If he tries to back-pedal from my blame, what are the chances that I would win the case?

Should I take pictures of the accident scene?

Were you injured, or just your car damaged?
You file a police report IMMEDIATELY so that you are on record for when it happened.
Then you file a civil case in Small Claims or regular civil court if over the small claims limit, and hope you can prove that you have the right person by the plate number.
Alternatively you file a claim with your insurance, and they file a claim with his insurer.

He might have his car fixed, and deny it all, and there's no telling what the result will be.

Did you call the police and give them the license #. The police will investigate.

Were you injured? Were you a pedestrian or in another vehicle? What were the circumstances of the accident. If you were in another vehicle, have you reported it to your insurer?

Note that it is a crime in most places to run from the scene of an accident in which your vehicle was involved without leaving your ID. Therefore you should report it to the police and get the police to investigate.