The Master Instructor, also known as Drillmaster in the GBA release, is an enemy in the Advance and Complete Collection versions of Final Fantasy IV. They attack in groups of eight during Yang's trial in the Lunar Ruins.
Rydia should summon Bahamut, or Palom and Porom should use Twin magic to whittle down their large HP quickly. Yang and Cecil should help with their physicals while Rosa or Porom heal. The Master Instructor's physicals are mediocre in strength, but the damage adds up due to their high numbers.