The clear plastic PCB (Printed Circuit Board) cover and the insert are all unclipped, as can be seen in the first photograph.

The battery is soldered to the PCB at the top near the button, as shown in the second photograph. The battery's tabs can be unsoldered using a good soldering iron, 60W or greater and desoldering braid/wick. You can use a solder sucker which may be quicker, but a cheap solder sucker can damage the board's pads.

Once the pads are unsoldered, you can remove the PCB from the casing and pry the battery out of its holder. You can use desoldering braid to clean excess solder from the pads so they are prepared for soldering in the new battery.