Find a high level Dinopithecus and kill lesser Dinopithecus around it. After 2-3 Beta Dinopithecus killed, it will prompt you to bring the creatures HP down to 85% or below. At which point you will be able to feed the Dinipithecus Raw mutton, or Exceptional Kibble. Enjoy your Monkey, and don't forget...these things can equip helmets!

More Dinopithecus Taming & KO Tips