How do I make a Neutral Knuckles Chao that looks exactly like Knuckles on Sonic Adventure 2 Battle without an action replay?

You don't.

In 2003 there was a give away in Japan where if you brought your memory card, Sega representatives would put a Tails Chao (also obtainable through the Fake in Yellow quest on PSO Eps 1 and 2), a Knuckles Chao, and an Amy Chao onto your memory card. All 3 are immortal and animals do not affect them whatsoever. So Action Replay and/or GameShark are the only ways to get the Knuckles and Amy Chao. Tails Chao can be gotten in the afformentioned quest in Phantasy Star Online Episodes 1 and 2, which is about 40 dollars used on Amazon.