If you want to master Wobbuffet, like I've mastered my Lv 82, you have to use strategy and it works for beating him to. Take for instance a Normal-type like Clefable, or Lickilicky, most of the attacks the trainers will give them are more than likely special,so try to start off with Mirror Coat.
A fighting type like Hitmonlee or Primeape, will more than likely have Swagger, to confuse the opponent, so you should have a back up plan.
Rock-types and Steel-types will have physical with the occasional Sandstorm attack.
Psychic/Ice/Electric/Fire/Grass/Water/Ghost/and Dark types are very hard to predict. Psychic-types will more than likely use a special attack, so use Mirror Coat, same thing with Ice-types.
Fire-types, like Magmar and Magmortar more than likely have the move Confuse Ray, so try to throw up a Safeguard and hope it doesn't hurt itself when you use Mirror Coat.
Grass types will more than likely use a status move, so use Safeguard, if you feel you should.
Water types will use special attack, unless it's a Gyarados, then you have to chose carefully.
Ghost-types will try to put you to sleep, so use Safeguard no matter what. Dark-types are tricky, so you have to act on your instinct when it comes to them.
And a Hypnosis attack + Shadow Ball helps, as well as a round of Bite and Crunch attacks, just be sure to put it to sleep/paralyze it/poison it/burn it first, and it's a good chance that it will hurt itself in its confusion. But be careful about Destiny Bond. Stall as long as you can until it either wears off or runs out of PP/turns
I hope this help some, since i used my past experiences with my Wobbuffet.