In Pokemon Black and White, the Elite Four can be battled in any order. The room to the northwest is the room of Grimsley, the Dark Elite Four Member. Use Fighting-type and Bug-type Pokemon to take him down.
In your first battle with Grimsley, he has a lv48 Scrafty, a lv48 Krookodile, a lv48 Liepard, and a lv50 Bisharp. The recommended level for your Pokemon to be at is lv53.
His Scrafty has Sand-Attack, Poison Jab, Crunch, and Brick Break. His Krookodile has Crunch, Dragon Claw, Foul Play, and Earthquake. His Liepard has Fake Out, Aerial Ace, Attract, and Night Slash. His Bisharp has X-Scissor, Metal Claw, Night Slash, and Aerial Ace.
After you receive the National Dex, you can challenge the Elite Four again, as well as Alder. His rematch team is: Sharpedo lv71, Scrafty lv71, Krookodile lv71, Liepard lv71, Drapion lv71, and Bisharp lv73. The recommended level for your Pokemon to be at is lv78.
His Sharpedo has Waterfall, Night Slash, Earthquake, and Aqua Jet. His Scrafty has Crunch, Poison Jab, Head Smash, and Brick Break. His Krookodile has Outrage, Earthquake, Foul Play, and Smack Down. His Liepard has Night Slash, Fake Out, Aerial Ace, and Attract. His Drapion has Poison Fang, Thunder Fang, Fire Fang, and Crunch. And finally, his Bisharp has X-Scissor, Aerial Ace, Guillotine, and Night Slash.