Meh, the E4 and moves against them.
1) Uses Dark: Make sure to not use a Psychic pokemon or move against this person. Have Fighting and Bug attacks at the ready. Electric and Fire are also good for the mixed types.
2) Uses Ghost: Dark attacks are effective against them. Just make sure to not use normal or fighting attacks.
3) Uses Ice: Have Electric (Thunderbolt), Grass, and Fire or have a good Rock type that is fast.
4) Uses Dragon: Have Ice attacks for his Dragons, they are all 4x weak.
5) Uses Steel: Fire types Fighting and Ground pokemon do wonders here.
Basically, have a good Electric, Psychic, Water, Fire, Ground, Rock, or Ice type and you will be fine (or just teach one of the above attacks to a pokemon that can learn it).
Also be sure to bring plenty of Revives, Full Restores, Hyper Potions and Full Heals. That's about it.