Okay how did you calculate that?
I didn't. I also couldn't because the only information given is that the demand is probably not that great and for only about an hour, and you have used some small cells without complaining that they didn't work. I still have no idea how the cells are arranged, or what on earth the 9v batteries do, or are supposed to do. The only thing you have been remotely specific about is the motors, which draw 200mA. They are probably not very powerful but, at 165 rpm, I imagine they have a lot of torque. I know you have four, I will assume they run continuously. They therefore draw 800 mA. In the absence of better information, I'm guessing the camera needs another 200mA and also runs continuously. That is a total of 1000mA, and thus 1000mAh if you do it for an hour..
A decent AA NiMH like Eneloop is good for 2000mAh and a typical 18650 LiIon is good for 4000mAh, which means the former (in theory) should deliver 2000mAh and the latter 4000mA for an hour.
In the face of the above, I guess the sensor can be neglected.
Similarly, whatever the servos take momentarily, I assume it is a lot less than what the motors take continuously and, if they need 1000mA momentarily, the batteries will stand the strain. Guess 200mAh.
So, with the AAs, that leaves 800 mAh @ 9.6v to drive the Mega, any peripherals you haven't mentioned, slack-arsed charging by you, and lies about the real capacity by the manufacturer. I don't think it sounds unreasonable but you I submit that you should get a decent 5v regulator, perhaps more than one.
if you add up all the volts required for each them it is well over 20 with motors,
You don't add volts, you add current. You only need to provide the recommended voltage, and hopefully it is the same for all devices, but if you draw too much current, the voltage will fall.
There is also amps that throws me off.
Evidently. See above.
That should give you something to work on.