Stroper's Sweep attack is strong and hits the whole party. It can inflict the party with Silence and Gradual Petrify. Quina Quen can eat it to learn Lv5 Death. Use of a Soft or Stona makes it "Too soft to live" and instantly kills it.
If no Softs are available the party may steal a Soft from it or use the White Magic spell Stona to defeat it. Otherwise, Fira and other Fire-elemental attacks are good. The player should keep the party's HP up above half, as Stroper's Sweep attack deals heavy damage to everyone. Attacking it physically will cause it to counter with Gradual Petrify.
Location: Black Mage N°123 (disc 4, inside Black Mage Village inn), Daguerreo, Disc 4 - Near Black Mage Village Item Shop - Black Mage No. 24