Much of what has already been posted I agree strongly with. Permit me to summarise a few salient points.
DO NOT:-
Try to do this by yourself
Withdraw co-operation
Let him hang himself by allowing him to make stupid mistakes
Suspend your professionalism
Do anything even remotely detrimental to safety (including ex-lax, eye-drops etc.)
Behave on stopovers in a manner that will invite a frosty atmosphere onto the flight deck next day
Allow yourself to become known as a crewroom whinger/moaner. Talk to people by all means, but make sure they are people who can address the problem.
DO:-
Make sure your own procedures and skills and knowledge are as high as you can get them
Stay courteous and professional at all times
Accept that, as the appointed commander, he, not you, is legally responsible for this aircraft, all crew and passengers
Keep communication going
Consult on the quiet with other FO's (you'll not be the only one with problems with a poor skipper)
Have a word with your union rep, Flight Safety Officer, Fleet Manager, or a senior Training Captain