One way that you can remove your bathtub faucet cartridge is by using a wrench and a screwdriver and prying it off. Sometimes you can loosen it up with a flat razor.
Turn off water, Remove handle (screw behind or under handle), use wrench to turn cartridge (usually opposite direction of turning on water. ) Slide out cartridge once loose.
changing a bathtub faucet cartridge is bit challenging, no need to close main pipe, just make sure only hot and cold water lines are closed, it is good to turn mainshower.