The new cartridge should come with a littlle plastic adaptor that slides over the stem of old cartridge after removing the clip.
The square end of this adaptor sticks out so you can turn it with a cresent wrench.
after locking the adaptor in there try spinning it both directions a couple of times first to loosen it up before yanking on it.
Lube the new cartridge up really good with plumbers grease before installing it to protect the o-rings.
If you find the hot/cold are reversed after installing it just remove the clip and spin the cartridge 180 degrees and reinstall the clip.
They also make a tool for pulling the cartridge just incase youre not feeling lucky