I was having a bit of difficulty with this one.
The root cause of my problem: I was killing the enemies TOO fast.
After the Vic Viper battle, ADA will tell you to go and get some Metatron a short distance away. Snag it, and an enemy will appear. Take him out.
The reinforcements will show up. ADA will suggest using the Gauntlet subweapon. Taking her advise is completely up to you, but this is where you need to s l o w d o w n
Take your time with these enemies, and be prepared for when ADA says that reinforcements are coming. When she makes her "estimated 90 seconds" for battle statement, press down on the left stick. Dingo will make a comment, AND THEN the timer will show up on the top right of the screen (1 min 30 sec.) Take out the remaining enemies and you will have an Ex Mission waiting above the entrance to canyon AND this trophy pop.
I can confirm that this can be done in a new game+ with Naked Jehuty. As a matter of fact, I recommend that frame, and using all subweapons from the jump. When you see the timer, switch to homing missiles and wipe everyone out in a flash.
Questions, corrections and neg vote justifications in the comments below.