While Ra's may appear a spritely 50 years old he has seen the passing of well over 400 years thanks to his use of the myserious Lazarus pit a bath of chemicals and poisons which when combined in a particular way heal and renew the human body. In his centuries of life he has built up an organiseation of fanatical followers that rivals the Vatican and The Order of St. Dumas for strength. Ra's has made it his goal to cleanse the world of it's overburdening population in an attempt to save the ecosystem, this translates as a wholesale slaughter of 99% of the worlds population or just under about 6 billion people.
Ra's intends to rule the future population but will not live forever and so has put a great deal of his energies into securing an heir and husband for his daughter Talia. At first Batman was his first choice, a man in peak physical condition with great force of personality, Ra's could see no one better to lead the world but Batman opposes the taking of life and so is one of Ra's greatest opponents, and possibly Talia's greatest love. Bane was Ra's second choice, but he was a brute and a poor reflection on his predecessor. Azrael is the most recent candidate but was dismissed because his DNA contained animal genes.
Ra's does not usually engage in combat himself but will use various weapons should he be forced to, he is likely to engage in combat with a sword, most likely a falchion.
Ra's is a physician and a skilled combatant. He is nearly immortal, with the use of the Lazarus pit, and has used this time to learn much.
Ra's plans are so grand that thwarting the smallest part of one may set him back years, but if there is one thing he has plenty of it is time.