Moves like Double Team, Protect, and Toxic can be learned by almost anything. It's overall not that hard to come up with a team that can take advantage of evasion. Tanky evasion mons will laugh at the low BP moves that ignore accuracy. Just have stuff to take care of taunt and you should be good to go.
Now go make people cry salty tears in rated wifi battles where the evasion clause can't touch you =)
Off the top of my head, you could make a Sandstorm + Evasion team. Abuse Sand Veil and Toxic with Gliscor, Garchomp, and Cacturne. The 8 turns max of Sandstorm hurts it, but I'm sure you could just add Sandstorm to your team's movesets.
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Considering that I am using a unevolve pokemon. One lesson I learn from Double team is that all you need to do is strike strike strike. It doesn't matter if you miss, it will bound to hit sooner or later.
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Moody pokemon are the way to go, I think. Bidoof, Glalie, Octillery, and Smeargle can all get it. You have a random chance of getting a +2 evasion boost every turn and you can add in some double teams for good measure if you want
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