since trying to get all 8 billion+ humans to agree on a plan of attack would be a near-impossible task.
We wouldn't need even close to that many humans. Just a couple of million people (the size of a medium-large military force) with the proper funding could probably kill off all of the large to medium animals within a few decades.
Killing of all the arthropods would be more tricky and we probably couldn't completley eradicate them just because we wouldn't be able to find them all.
Of course that's purley for winning in a direct confrontation. Without any animals we'd probably go extinct not long after, so it's not really a win in the end.