Once you've entered the Hall of Fame and traveled to Stark Mountain, you can revisit the Pokemon League for a rematch with a stronger Elite Four and Champion, all of whose Pokemon are the same but with a 15-16 level increase.

ELITE FOUR BATTLE 1
vs. Aaron
Yanmega (boy) Lv65 BUG FLYING type Effective move types: ROCK FIRE ELECTRIC ICE FLYING types
Drapion (boy) Lv69 POISON DARK type Effective move types: GROUND type
Heracross (boy) Lv67 BUG FIGHTING type Effective move types: FLYING FIRE PSYCHIC types
Vespiquen (girl) Lv66 BUG FLYING type Effective move types: ROCK FIRE ELECTRIC ICE FLYING types
Scizor (boy) Lv65 BUG STEEL type Effective move types: FIRE type

ELITE FOUR BATTLE 2
vs. Bertha
Whiscash (girl) Lv66 WATER GROUND type Effective move types: GRASS type
Gliscor (girl) Lv69 GROUNG FLYING type Effective move types: ICE WATER types
Golem (girl) Lv68 ROCK GROUND type Effective move types: GRASS WATER ICE FIGHTING GROUND STEEL types
Rhyperior (girl) Lv71 GROUND ROCK type Effective move types: GRASS WATER ICE FIGHTING GROUND STEEL types
Hippowdon (girl) Lv68 GROUND type Effective move types: GRASS WATER ICE types

ELITE FOUR BATTLE 3
vs. Flint
Rapidash (boy) Lv69 FIRE type Effective move types: WATER GROUND ROCK types
Houndoom (boy) Lv68 DARK FIRE type Effective move types: WATER FIGHTING GROUND ROCK types
Flareon (boy) Lv71 FIRE type Effective move types: WATER GROUND ROCK types
Magmotar (boy) Lv73 FIRE type Effective move types: WATER GROUND ROCK types
Infernape (boy) Lv71 FIRE FIGHTING type Effective move types: WATER GROUND FLYING PSYCHIC types

ELITE FOUR BATTLE 4
vs. Lucian
Mr. Mime (boy) Lv69 PSYCHIC type Effective move types: BUG GHOST DARK types
Espeon (boy) Lv71 PSYCHIC type Effective move types: BUG GHOST DARK types
Bronzong (boy) Lv70 STEEL PSYCHIC type Effective move types: FIRE type
Alakazam (boy) Lv72 PSYCHIC type Effective move types: BUG GHOST DARK types
Gallade (boy) Lv75 PSYCHIC FIGHTING type Effective move types: FLYING GHOST types

CHAMPION
vs. Cynthia
Spiritomb (girl) Lv74 GHOST DARK type Effective move types: NONE
Togekiss (boy) Lv76 NORMAL FLYING type Effective move types: ELECTRIC ICE ROCK types
Lucario (boy) Lv76 FIGHTING STEEL type Effective move types: FIRE FIGHTING GROUND types
Garchomp (girl) Lv78 DRAGON GROUND type Effective move types: ICE DRAGON types
Roserade (girl) Lv74 GRASS POISON type Effective move types: FIRE ICE FLYING PSYCHIC types
Milotic (girl) Lv74 WATER type Effective move types: GRASS ELECTRIC types

Hope it helps!