Of the many times I've been shot by the Adversary's homing Brimstone, I've managed to avoid it just a couple of times. So, I know it's avoidable, but I don't know how to do it reliably.
Usually when I get there it becomes a power check: if I can dispatch him before letting him shoot his first Brimstone I have good chances to end the run victorious. The problem is I'd like to have a chance to end even those runs when I have less firepower, but usually in those cases if I get the Adversary my run stops there.