Here is a list of the tools I use.
An old Radio Shack 100W soldering gun.
A desoldering pump or what I call a solder sucker.
A "pig sticker" chisel or other 1/2" wide chisel
You need to carefully heat the tab area and use the solder sucker to remove as much of the solder as you can. This requires you to continually push the primer of the sucker down until it clicks and placing the tip near the solder gun tip and clicking the trigger to have the solder be sucked into the chamber of the sucker. You then prime the sucker again for the next shot. You will probably need to pull the cooled solder from the tip of the sucker after a successful extraction since the liquid solder will cool and form a small cylinder of solder which is ejected (mostly) from the tip when the pump is primed. You need to keep moving the solder gun tip since it is very hot and will damage the battery if left in one spot too long. After you've removed most of the solder, you then use your chisel to lift the battery tab from the pad area of the printed circuit board and then pull the battery down to extract it. It took close to 30 seconds for the solder gusto heat the solder tabs enough to liquefy the solder so be patient and work quickly. Remember tho move quickly and everything is very hot!
From left to right, solder sucker, flux, pig sticker, solder sick, extracted battery, soldering gun.
Pack before extraction