It's a challenge based on something pretty uh... Unique... I guess. The comic doesn't explain as much as it should.
>Pick up the first pokemon you see in an area. Catching two from the same area is not allowed, iirc.
>Release the pokemon if it ever faints, you can't force them to faint. You must TRY to use them, that's a part of the challenge.
>You must nick name them ALL and the nicknames can't be similar to another. (LOL1, LOL2, LOL3 = no go)...