Heat up your soldering iron to around 350 Celsius (400-500 is okay but you should be faster & more careful). Add a bit of solder to the tip of your iron (this helps heat transfer).

Press the tip of your iron against one of the solder joints, the more surface area you can provide to the solder joint, the faster it will melt.

It can help to lift up on the battery and/or tab with pliers/tweezers while melting the solder to pull it off the cartridge as soon as possible; The less heat to the cartridge the better.

Be sure not to get your solder iron anywhere near the other components! you don't want to melt the black plastic rom casings or mess with the other components

This step is shown with just the tabs, but the process is the same if your battery is still connected to the tabs