I would assume he has a Lum berry hidden in his mouth or something similar. I wouldn't put it past Alex to do something like that, especially against a ninja.
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I either guess that he did some secret Poison resistant training with Crobat or that he either drank a Potion that gives a Poison resistant effects or nulling the Poison's effect... or something more weird like his System just casually removes it...
I am really curious as to how Alex avoided total paralysis from the poison. He wasn't affected at all and I am sure he planned this out. I also wonder if Ditto will be used as a trumph card. Ditto can make a last minute assualt. Gardevoir will use Heal Pulse on the girlfriend.