For anything to run long on a battery it would have to put the RPi to sleep when not used for it's purpose (like no movement detected).
However, you can see that this approach then requires the Pi to boot-up again, which can take 25-30 secs with a standard Raspbian image - which means your subject could be long gone by then.
I tried once (just for the heck of it) hot-wiring an ATTiny chip to a motion sensor and a cheap keychain camera (with micro-SD storage) to make it take either a sequence of pictures or some limited-time video clips when the sensor detected motion (it was more sensitive than the motion detection built into the camera). The time to wake up the ATTiny and power-on the camera to start taking vid was about 12 secs (mostly waiting for the cheap camera to start taking vid - it required press/hold a few secs of a button to signal the camera to start recording, which was automated via the ATTIny). The sensor drew <50ua waiting to trigger the sleeping ATTiny.
CORRECTION: It took about 6 secs to start taking vid. 12 secs was the time gap between the end of a vid, powering down, and then immediately powering up again to take another vid.