Zombor's Upper Body is weak to Water and 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 Light, so you'd be better off having learned Fire Sword (with Crono and Lucca) to beat that part. Marle and Lucca's Dual Tech Antipode Bomb, which has Shadow magic element type, can cause some very good damage to the Upper Body.
If you defeat the Upper Body first, it will steal all the MP from the party member who defeated it and the Lower Body will start to use an attack that instantly kills one of your party members. Hence, it's better to defeat the Lower Body first. You would typically have two of the party members use magic or Dual Tech based on the weakness of the part, while having the third party member do physical attack or heal.
When the players fight Lavos, Lavos becomes the strength of some of the bosses you faced in the past. One of them is Zombor.