Carefully lift the battery from the side nearest the four gold contact pins, but don't try to fully remove it yet.

At this point, the battery remains connected via four wires to the power supply board.

Carefully desolder the four wires from the power supply board in order to completely detach the battery. There is very little room for the soldering iron without damaging the case or the board; you may want to remove the board first.

For help with soldering, see the soldering guide.

Alternatively, you may remove the battery and power supply board together, without any soldering, but access requires some additional disassembly while carefully leaving the battery connected via the wires the entire time.