How to Defeat the Elite Four and Champion- Pokemon Black/White Version
Shauntal the Ghost Trainer
You can fight them in any order but let's go clockwise in this guide just to make it easier on everyone. This would make Shauntal first, with her ghost pokemon.
She has 4 pokemon with the first being Confagrigus at level 56. Then comes a Drifblim at 56, Golurk at 56, and Chandelure at level 58.
If you are in the Challenge mode raise all the level 56 to 60, Chandelure is now 62, and she has a level 60 Banette added to the team.
In order to win, a dark type or any pokemon with Ghost moves would be helpful, if you don't choose to try and tank it out. Remember no normal type moves without something helping them hit. ;)
Grimsley the Dark Trainer
Next up is Grimsley, with his Dark type pokemon.
He has a level 56 Liepard up first, a level 56 Scrafty, a Krookodile also at level 56, and a level 58 Bisharp to end his team.
In challenge mode, all the level 56 are brought up to 60, Bisharp is 62, and a level 60 Absol is added to the team.
Best way to go against Grimsley is with Fighting or Bug type moves, unless you have a pretty strong pokemon that gives or takes good hits.
Caitlin the Psychic Trainer
Third trainer in our clockwise journey is Caitlin. She uses psychic pokemon.
First up on her team is level 56 Musharna, also level 56 are Reuniclus and Sigilyph. She ends her team with a level 58 Gothitelle.
Challenge move brings all the previous pokemon to level 60 and adds in a level 62 Metagross.
If you got a dark or bug type for the previous two battles, use them again, they will also be helpful here.
Marshall the Fighting Type Trainer
Last up, or first if you chose to start in the opposite direction, is Marshall. He focuses on the fighting type and none of his pokemon are dual-typed.
He has a level 56 Throh first, followed by level 56 Sawk and same level Mienshao. His level 58 is Conkeldurr.
Challenge mode has Throh, Sawk, and Mienshao up at level 60, a new level 60 Lucario, and Conkeldurr went up to level 62.
Best types to use would be a flying type or psychic type moves, just watch out if you use flying pokemon as they know some rock moves.
Once you beat all four of the previous trainers heal up and restore PP if you have the items, it's time to face the champion.
Champion Iris and her Dragon Type Pokemon
Iris is the name, don't forget it. She has a full party of dragon? pokemon. They look like dragons anyway, even if only 3 are typed as so.
Level 57 except for one, Hydreigon, Druddigon, Archeops, Aggron, Lapras involved. The last pokemon is a level 59 Haxorus.
Challenge mode has all the level 57 as 61 now and Haxorus is level 63.
In order to win you should have some nondragon pokemon with dragon moves to take out her three dragons.
Hydreigon could also be taken out by ice, fighting, or bug moves. Psychic won't affect him, fire, water, electric, grass, ghost, and dark are all halved damage.
Druddigon is weak to Ice and dragon, but only takes half from fire, water, electric, and grass.
Archeops is weak to water, electric, ice, rock, and steel. Ground won't affect him at all, and normal, fire, poison, flying, and bug are all halved.
Aggron is 4x weak to ground and fighting so if you have those it's your best bet, if not he's also weak to water. Don't use poison as it won't do anything, normal and flying only do 1/4 damage. Ice, psychic, bug, rock, ghost, dragon, and dark all do half.
Lapras is weak to electric, grass, fighting, and rock, water is halved, ice does 1/4 damage.
Haxorus is last, weak to ice and dragon moves. Half damage is dealt by fire, water, electric, and grass moves.
So in summary, you might want to bring along your bug pokemon first up to take out Hydreigon, You may want an ice type for Druddigon, Haxorus, Archeops, and Hydriegon (if you have no bug or it faints trying to kill him). A fighting type could help you with Lapras and Aggron or a rock type for Lapras and Archeops.
Hope this helps you win! If you did, congratulations new champion! *throws confetti*