Whats the problem?

I know the batterie is on its way out. but I have had a full charged good car batterie on it and it will run an start. the problem is when its running.(with good batterie). I have not rode it more then 10 miles since I changed the alternator and rotor so have not had a good road test on the alternator. It is firing on both cylinders. I have taken the plug wire off of both and will keep running with one on either side. I will be hard to test the alternator in neutral as it bog and stumble at about 40k and drops to 20k then idle fine until I give it throttle again and will repeat at 40k.

I am having a hard time envisioning a cylinder actually running in spite of so much excess gas it is spitting from the exhaust.