Ghostbusters: Spirits Unleashed Ecto Edition

Using the method hidden beneath, I found the easiest way to attain this achievement was to group all the Busters together and have them focus on reviving each other.

Sabotage their proton packs where you can and as the last buster is being revived (Or timed well so that your attack will down all 4 busters) Save your Ultimate for this moment.

Doing this along with the method below indirectly helps as they're too focused on reviving or recharging protons and/or batteries.

Only the final group slime counted directly in the progress tracker for me, to see them count you must re-enter the ghost realm after the match.

One important thing to take into account is that the Ultimate attack countdown can be negated by being trapped and rifted. Once you respawn you will have a full Ultimate charge again, however you should down the group with normal attacks a couple of times before attempting the Ult attack again.
To negate the wait time you could rift yourself by letting them trap you or end the game and restart.

The count seemed to be affected by factors that I have not determined. Though from what I could tell simply leaving the game after getting your first down DID NOT appear to count towards the count. So I believe you must finish the game for your downs to count. Again this is unconfirmed and your mileage may vary.