Zombor's Upper Body is weak to Water as well as Shadow, so you'd be better off having learned Ice Sword (with Crono and Marle) already.The same is with the Lower Body, but it's weak to Fire and Lightning, so you'd be better off having learned Fire Sword (with Crono and Lucca) to beat that part. It's better that you defeat the Lower Body because the Upper Body will steal all the MP from anyone who defeated it. You only need to take care about the Upper Body's attacks, they can be powerful!
If you defeat the upper body first, then Zombor will
start to use an attack with the lower body that instantly kills one of
your party members. When fighting Zombor, have a good supply of Mid Tonics and Revives. You'll need them.