Lorelei
The first member of the Elite Four uses exclusively Ice-type Pokemon on her team. Include at least one Pokemon on your team of the Fire, Fighting, Steel or Rock type. Ice Pokemon crumble when they are hit with those types of attacks. Examples of monsters that can defeat her team relatively easily include Magmar, Lunatone, Hitmonchan and Magneton. Lorelei's Pokemon team consists of Dewgong, Cloyster, Slowbro, Jynx and Lapras.
Bruno
Bruno, the second of the Elite Four, is a master of hard-hitting psychical attacks. He uses mainly fighting-type Pokemon, along with a pair of Onyx. A Flying or Psychic Pokemon can knock out his Hitmonchan, Hitmonlee and Machamp. Any Pokemon with a strong Grass, Water, Fighting, Steel, Ground or Ice attack should be able to handle the two Onyx. Gyrados, Exeggutor and Starmie are good choices for this battle.
Agatha
A user of toxic Poison Pokemon, Agatha relies on status altering moves that cause Confusion and Poison to win. As dangerous as her Poison Pokemon are, Ground and Psychic moves cripple her lethal team of Golbat, Haunter, Arbok and pair of Gengar. Note that Golbat is unaffected by Ground attacks. Steel Pokemon are also effective in this match, because Steel Pokemon cannot be poisoned. Consider bringing creatures similar to Steelix, Nidoking and Grumpig to fight Agatha's Pokemon team.
Lance
Lance is the Dragon trainer who is the final member of the Elite Four. His dragonlike Pokemon are all powerful and fast creatures with fewer weaknesses than most. Lance uses a team made up of two Dragonair, a Gyarados, an Aerodactyl and a mighty Dragonite. Ice and Electric Pokemon are the best way to finish off these monsters because most of them are also Flying type. Some Pokemon that would defeat Lance's Dragons are Electrode, Walrein and Raichu.
Rival
After defeating the Elite Four, you will be challenged by the current Champion, your Rival. Your Rival's Pokemon team will be different depending on the Pokemon you choose at the start of the game. Rival has a balanced team with no glaring flaws. An Alakazam, Rhydon and Pidgeot will always be on his team, while Exeggutor, Gyarados and Arcanine appear on the team to supplement the creature he choose at the start of the game. With the stable team you used to defeat the Elite Four, you should not have a problem beating your Rival one more time. Just keep in mind what Pokemon types have an advantage over others, switch out Pokemon as you need, and use heath-restoring items after every battle to keep your team strong.