Make sure you are wearing an anti static wrist strap, or make sure you are grounded. You are working close to the logic board, you do not want to cause static discharge damage!

Using your spudger, easily pry the battery cable from the connector. You may hear a click, this is normal. There are two snap in spots that keep the cable fastened tightly to the board.

I found it easier to slide the spudger under the side of the cable and lift gently. It only lifts a little of the cable at a time. I then moved the spudger to the other side of the cable and repeated. It gently disconnects from it's connector this way. (shown in picture 2)

Unscrew the four screws with your PH0 bit. Set them inside the case piece as it should prevent the screws from rolling around.

Once the battery is free, life the edge with the spudger and gently life the battery out of the chromebook.