Before you challenge the Pokémon League, use the Dowsing Machine app on your Pokétch near the base of the waterfall to find the Sky Plate. Now, use Surf and Waterfall to enter the building. Before going to the receptionist make sure to have a very good well-balanced team. Also make sure that all the members of your team are trained around Levels 54-58 to be able to stand a chance of succeeding. Also stock up on Hyper or Max Potions, Full Heals, Revives, and Full Restores. Just before you get to the receptionist in front of the door leading to the Elite Four, Barry will appear and challenge you to determine who among the two of you is more worthy.
The main new change is that Barry's Munchlax has evolved into a Snorlax, which should help count Snorlax as seen in the Sinnoh Pokédex. Snorlax can be easily brought down by a powerful Fighting-type attack such as Cross Chop or Close Combat. Other than that the same weaknesses as before can be used to defeat the other members of his team. Afterwards Barry will leave convinced he is not ready yet if he keeps losing like this, but vows to be the one to defeat you.
Talk to the Ace Trainer and once he confirms you have the eight Sinnoh Badges you can then face the Elite Four, but just remember that if you lose after passing through the doorway, you must start over.
For dealing with Bertha's team if you have a fastGrass or Water-type, then you should have an easy time. Whiscash has a 4x weakness to Grass-types, Golem, Rhyperior have a 4x weakness to Grass and Water-types, and Gliscor has a 4x weakness to Ice-types. Exploit these weaknesses with attacks such as Ice Beam or Surf. Hit Hippowdon, her only single type Pokémon, with powerful attacks before it can hit back. While Gliscor, Golem, and Rhyperior know moves to cover several of their weaknesses, their low Special Defense can still be exploited.
Flint will thank you for helping Volkner earlier and then face you in a battle. Be careful when his Pokémon use Sunny Day, as it can raise their Fire-type moves and weaken the power of Water-type moves. His first Pokémon Houndoom should be taken down as quick as possible to help give you an early lead before Sunny Day is used. Flareon should not be much of a problem, though be careful with Overheat since it is very powerful when first used. Also its Will-O-Wisp can weaken your Pokémon's physical moves by half and cause minor damage each turn. Rapidash's speed can be a hassle, and its Solar Beam can cover its weaknesses, especially in harsh sunlight. Infernape is weak to Water, Ground, Flying, and Psychic, but it can cover Water- and Flying-types with Thunder Punch. His strongest Pokémon Magmortar has a pretty strong moveset and Special Attack, but a faster Pokémon with a strong Water, Rock, or Ground-type move could easily take it out.
Cynthia will thank you for your help on Mt. Coronet and in the Distortion World earlier before facing you. Cynthia does not follow a specific type so this battle will be trouble if your Pokémon's levels are not high enough. Spiritomb has no direct weaknesses, though a Steel-type can be quite effective. Roserade shouldn't be that much of a hassle if you get it down quick with Fire or Flying types. It would be recommended to use an Electric-type against Milotic since it has Ice Beam to counter Grass-types. Physical attacks, like ThunderPunch or Wood Hammer, tend to work better because they make Mirror Coat fail.
Use Fire, Ground, or Fighting-type moves to bring down Lucario. Togekiss can be brought down by an Electric-type but be careful of its high defenses. Garchomp, the Champion's strongest Pokémon, is far more dangerous than anything you have battled. It may have a 4x weakness to Ice-types, but its high physical Attack and Speed often lets Garchomp one-shot your Pokémon before you can move. If you can get it to use Giga Impact, then exploit the free turn while you have the chance.
After the battle Cynthia will praise you on the conviction you have with your Pokémon to become Champion. She'll then take you to the Hall of Fame where Professor Rowan will join you and all the Pokémon on your team are recorded into the Hall of Fame.