I've seen a few posts on how to do this but they all seem overly complicated, for example using the battery controller or wiring a USB cable to the battery terminals directly.
The trick is to find the 5 volt rail coming from the USB input and solder a cable from that to the battery positive input on the board.
The only place I could find an output for the 5 volt rail from the USB input was under the ribbon cable shown below. The bottom right test point (golden circle) did the trick. You'll need to remove some of the insulating tape and unscrew the ribbon cable to access it, it's a bit of a tight soldering spot, so use a fine tip and don't turn the heat up too much. There might be a better spot somewhere else on the board so have a sniff around but I couldn't find one easily.
Then you just need the terminal header for the first red cable on the left of the battery input, solder the wires together, insulate the join with some electrical tape and that's it. You can now boot up and use your Nexus 9 without a battery, just by running off the USB cable.
Here's the Nexus 9 running the RTSP stream from the back yard pool camera.