For others' benefit, I'm copying the text from the Chapter 58 procedure for those wondering what the strategy is the first time you encounter Minister Tsuchino-Homare:
"He's completely invincible. Fight for 3 turns and a cutscene will trigger to progress."
Note that there is no followup battle, so you will get a chance to heal/adjust party.
Later, when you return to fight again:
- He starts off weak to wind and blunt, resistant to magic. HP stopper at 50%
- He switches patterns at half health, turning resistant to his previous weaknesses but also becoming vulnerable to magic.
- His defeat yields an already awakened T3 "Physical Resistance+ (Katana)" Grasta.