Well fondant is completely right, you can practically beat the Elite 4 with one Pokemon as long as it is over level 70. However there is a Pokemon that can deal with the Elite 4 exceptionally well. It is frankly easy to obtain and it is a total powerhouse. This Pokemon is called Haxorus. Yes, Haxorus can deal with the entire elite 4 with relative ease as well as take on Iris.
However it is recommended that you EV train it in both Attack and Speed so that you are guaranteed to KO everything. Seeing as the Elite 4's Pokemon are all only fully IV trained and not EV, you will outspeed everything anyways however you might like to know that Shauntal's Chandelure is scarfed and shadow ball might just hurt a little.
Haxorus @ Life Orb
Trait @ Mold Breaker
EVs: 252 Stk / 252 Spd / 4 HP
Adamant/Jolly Nature Nature
- Dragon Claw/Outrage/Dual Chop
- Brick Break
- Dragon Dance
As you might already know, Iris' Haxorus is holding a Focus Sash and for this reason I recommend Dual Chop. After one Dragon Dance you can practically sweep her entire team with out, barring Lapras and Aggron. You could also go for Outrage for that raw power but it is at the cost confusion. Earthquake is in fact your best move as you will e able to hit any non-flying type Pokemon as well as deal heavy Damage. It is a very powerful and reliable move and you will also be killing the most Pokemon with it including Aggron and Metagross. Brick Break is just for that extra dazzle of coverage and mostly to deal with Lapras who has the potential of ruining your solo-run
Another nice option should be Volcarona. I am pretty aware that Volcarona has no direct supereffective move against Dragon and Ghost but she can deal with them extremely well as we all know how dangerous this moth can be after one Quiver Dance. However like a I mentioned above for the best results you would like some EVs in both Special Attack as speed however Volcarona's natural offensive presence will make you win anyways.
Volcarona @ Life Orb/Leftovers/Focus Sash
Trait: Flame Body
EVs: 252 SpAtk / 252 Spd / 4 HP
- Quiver Dance
- Fire last/Fiery Dance/ Flamethrower
- Bug Buzz
Quiver Dance is the key to succes. After one Quiver Dance, Volcarona is powerful enough to take down the entire league. Perhaps this is how Alder became Champion? Fire Blast/Fiery Dance/Flamethrower is for some Fire Power and is there for some STAB and will deal with little menaces such as Metagross, Aggron, Froslass etc..etc..Bug Buzz is the move that you will tend to use the most when facing Grimsley and Caitlin and will finish the battles quite fast. Psychic is for that extra coverage and will enable Volcarona to hit the Fighting types hard, however you should be wary of Stone Edge as it will knock this bug ug out of the sky. For this reason I suggest running the Focus Sash on Volcarona when facing Marshal as his Sawk has Sturdy.
You can basically beat the Elite 4 with any Nature and no EVs but I just suggested these since they are most likely your best options