Lorelei is the first of the Elite Four that you must battle. She specializes in Ice-type Pokemon. Although Fire-type attacks are Super Effective against Ice-type, most of Lorelei's team either resists or has coverage to Fire-type Pokemon. So the best option would be bringing good Fighting-type Pokemon like Lucario or even Machamp, or you can bring Aura Sphere users like Mewtwo and Dialga.
Bruno is the second of the Elite Four that you must battle. He specializes in Fighting-type Pokémon. Some tips are to have Psychic-type Pokémon like Mewtwo. The best move to use would be Psystrike. Good Flying-types like Mega Charizard Y work as well since most Flying-types are fast, and Heracross and Breloom are 4x weak to Flying-type moves. However, be careful of Lucario if your Flying-type doesn't have any Fire, Fighting or Ground type moves, since Lucario resists a lot of the Fighting-type weaknesses, and if you are running Pokémon like Charizard or Moltres, be wary of Keldeo, as one Hydro Pump could 1HKO your Pokémon.
Agatha is the third of the Elite Four and she specializes in Ghost-type Pokémon. It is recommended to bring fast Dark-type Pokémon like Weavile (as listed below) however Agatha'sGengar has Focus Blast, a base 120 power attack that can one shot your Dark-type but only has 70 accuracy. Also, Agatha'sGiratina has Aura Sphere, which never misses.
Lance is the last of the Elite Four and he specializes in dragon type Pokemon. Although he is the master of Dragon types, he doesn't have the Master Dragon type, Rayquaza. All of his pokemon are VERY fast. The strategy for him is to actually fire his medicine back at him and use high attack and speed dragon types like Haxorus or Dragonite after one Dragon Dance. However, Lance's Kingdra has Ice Beam and Dragon Pulse to counter most Dragon types. Also, Lance's Salamence has the Intimidate ability which will lower your attack stage by 1, so Dragon Dance twice and hope that Kingdra doesn't Ice Beam or Dragon Pulse you.