The Corrupted Empress

Another possibility would be to have a Buccaneer use Backspin Blow > Barrage > Backspin Blow > Barrage..... on the summoned job instructors and keep them away from everyone else so they can focus on killing Cygnus Empress. It'd also be possible to have someone of another class shove them all into the corner, if you want the person to possibly survive it could be a Paladin. Though having one person be the sacrificial lamb, assuming the bosses would continue to attack the one character like most mobs do after they've died, is another possibility. For looting it'd be possible to have someone with a pet + some move with invincibility frames loot everything that's near the Job Instructors.

Though it's possible this wouldn't work out too well if the different status effects can still hit without needing to do damage.