I have a 200 amp panel that is aluminum wiring. I had an air conditioner installed, and although it is on it's own breaker, it blows the main, not it's own breaker. It runs for a short time, but it always pops the main, even if almost nothing else in the house is running. Do I need to replace the main breaker, or is the problem more serious?

I think you will find that there is a loose connection either on the line or load side of the breaker. Loose connections tend to heat the metal connector and wire, and the heat is transmitted or conducted into the breaker. Breakers have a thermal component to them and will trip when enough heat is sensed.

It is possible the breaker is defective, burnt or dirty contact surfacer inside can raise the resistance of the contacts and again created heat.

You may try tightening the lugs holding the wire, be sure to tighten the lugs to the breaker also. I had found a nut bolting a breaker tab to a bus bar in a 200 amp GE residential panel, only had 20 amps on it, and it was loose enough to create enough heat to trip the breaker. I found this using an infrared detector, with only idiot lights. Nowadays I use a real Flir infrared camera to find hot spots caused by loose connections.

Working on the line side of the breaker will require the line to be shut off. This usually is done by pulling the meter. Once the line is de-energized at the breaker, then all the connections can be checked. Each lug and wire connector will have it's own torquing spec.

If the connections are not the problem, the breaker may need to be replaced. This can be confirmed using a millivolt tester, or a low resistance ohm-meter. Either can be used to detect high resistance at the contact points.

None of this is really is for a DIY'er.The utility may be needed to pull the meter, this is something a DIY'er should never tackle. The connections will require a torque wrench or torque screwdrivers. And the test instruments are expensive. Anything less than using the proper equipment will be guessing.