So you saved the world, but guess what? Technically you didn't beat the Pokemon League, because you never fought the Champion. Even though beating N who beat the Champion clearly should have made you the Champion. But presumably the paperwork was too complicated, as they want you to do it all again.
Which... wouldn't be a problem if the Elite Four hadn't suddenly brought out their real teams, which are 20+ Levels higher than what they originally had. Needless to say, it's going to be rough... and it might be wise to do some other postgame content before demanding a rematch, lest you want a beating.
South-East: Marshal the Fighting-type Expert
Marshall gains Breloom, who's 4x weak to Flying, and Toxicroak, who's 4x weak to Psychic. If you have both these types in good condition, this battle shouldn't cause much stress. But do watch out for Sawk's Sturdy ability (no OHKOs) potentially causing headaches.
North-East: Caitlin the Psychic-type Expert
Sleepy Caitlin adds Bronzong and Metagross to her roster. These Steel-types aren't weak to Bug, Dark or Ghost moves, but a good Fire or Ground type will put them out of their misery. Her other Pokemon can be dispatched with the aforementioned types, but no Bugs for Sigilyph.
North-West: Grimsley the Dark-type Expert
Grimsley's Sharpedo can easily knock the breath out of you, so throttle it with a fast Electric type or sturdy Grass type. His other addition, Drapion, has an interesting type combination; beat it down with Ground moves to ensure a safe win. His other Pokemon fall quickly to a strong Fighting type.
South-West: Shauntal the Ghost-type Expert
Spooky Shauntal has brought along Froslass, who's also weak to Fire, Rock and Steel, and Drifblim, who's also weak to Electric, Rock and Ice. Again, Dark Pokemon will scare her ghosts away, or you can target their secondary types if that way's safer.
Finally, the moment you've probably been waiting for: the chance to go toe to toe with Unova's reigning Champion! If you beat N and Ghetsis (and Cynthia), beating Alder should be a doable task. Like most champs, his team is quite varied, so be sure to mix and match.
His toughest Pokemon are Bouffalant, who's a menace to all but Ghost and Fighting-types, and Volcarona, who you should know very well from Relic Castle. Against this fabled Pokemon, Rock moves will do 4x damage or end it quick with Flying or Water moves before it gets pumped.
Congratulations on becoming the Champion!