There seems to be two contacts that snap into place. One is in line with the led pretty much in the middle of the phone and the second one in line with the camera lens on the opposite side to the lens. The middle one for me snapped pretty lightly, but the side one required a bit more pressure. After that the nfc started working again. Thanks for posting this!
I'll second the flathead screwdriver. Tried different plastic tools only to damage both the battery and a spring connector on the phone. With the flathead screwdriver battery came out quite easily lifting from the bottom end. There is an adhesive tape holding the battery firmly in place that retains the adhesive surface after removing the battery, so the new battery should attach properly.