Barnabas-Z is a boss in Final Fantasy IV. After being defeated by the party, Barnabas loses his head, which results in Dr. Lugae stepping in to take control of his creation himself. It is possible to miss this boss, if the doctor is defeated first, or quickly after Barnabas.
The player should attack Barnabas-Z at every opportunity. The damage caused when it explodes is equal to however much HP it has left, so at best the player will take it out before it detonates, and at worst one will be minimizing however much damage is caused by the explosion.