My 2003 Mazda6 is shaking/jerking when going up hills. It still accelerates normally but it is alarming. The car also kicks slightly when idling and the rpm needle goes up and down slightly.

Yes it could be a transmission issue. It could also need a tune up or have a plugged catalytic converter. Any check engine lights on?

Yes, the check engine light is on. I haven't checked it in a while but the last time I did it was a code for the catalytic converter.

Well there you go. It's probably a plugged converter. When they get plugged it's literally chocking the engine. So when you go up a hill the engine cant "breathe" like it needs to. Take it to a REPUTABLE mechanic to make sure that's all that's wrong with it

And don't delay. TransAm77 is right, I just want to add keep driving with a plugged cat and you will do more damage to your engine= cost