Mega Beedril V. Mr. Mine is cinched out because the Psychic bonus against poison cancels out the Bug bonus against Psychic...But not the Poison bonus against Fairy. Mr. Mime is basically a decayed husk.
@The Nonexistent Tazz
This is a tie cos there is no double super effective. :( I *think* the only Pokemon capable of beating it are fully evolved bugs that don't have poison as a secondary type (butterfree, scyther, pinsir). Psychic/Fairy (and Psychic in general) is a really strong type when there are no dark types or non-poison ghosts. xD