Format the card, in the P3. Then remove it, and unzip the firmware. You should put the .bin file, in the root directory. NOT in a folder.
Once starting the P3, the update process should start. Don't shut it off, during update. Make sure the battery is near full charge.
Now, my RC, wasn't happy with my card reader, so I used a flash drive instead, then it updated.
EDIT: When update complete (Cam light stops red/green alternating) you should have a text file now on the card, it will say the outcome. You want "success" or maybe "successful"... don't remember anymore.