You can go there with all 3 members to kill them together, you will be sure you'll kill them all.
And other thing:
I tried this Quest lots of times. Seems like the npc in hardins academy bugs sometimes and does not give you enough "bingos"to proceed even if you do it 20-30 times...even if you have 75+ toons and you one shot the boxes still the same problem
So if you wont get enough bingos after destroying all chests, keep repeating...