@ThePhalanx, here's a post-Burgh challenge for you.
Shadowfax wants to prove that he is the best electric type pokemon. Therefore he must solo Elesa's whole gym without evolving beforehand.
EDIT: Update #2
-After rescuing the trio, I go to find my dream mist from the dreamyard. I run into Team Plasma and defeat them easily with my Pansear, as Otto has been boxed until I defeat Lenora.
-After getting dream mist and going through loads of conversation with Fennel, I head to route 3 where I hope to find a Pidove.
-As it is an odd numbered route it's a Nuzlocke route, so I can only catch the first pokemon I see. It's a Zebstrika. Ahh well.
-So I beat Cheren anyway with Pansear and then have to chase after Team Plasma. I catch a Woobat from Wellspring Cave. I call him Roman. So I start to only use Roman as he is part of my Water/Flying team.
-I level him up and then proceed to defeat Team Plasma.
-I go through Route 3 and arrive in Nacrene City.
-I catch Rose the Pidove and Timothy the Tympole in Pinwheel Forest.
-After levelling up and defeating all the trainers around, I decide to Challenge the gym.
So I can't use healing items against Lenora. I didn't expect this to massively hard, but it actually was. I lost the first game to an unlucky crit against Rose, my (now) Tranquill. And the second game, her Watchog managed to defeat me thanks to that annoying hypnosis. I took healing items to mean berries aswell so I didn't use my chesto berries.
In the third game, I formed a better plan. I sent out Roman first against her Herdier and used it to just weaken it to red health, which meant that my Tranquill didn't suffer Intimidate and Lenora wasted her super potion on Herdier instead of Watchog. Roman was knocked out and I sent Rose in. I used Work Up as she healed herself, and then Work Up again as she missed with Take Down. That was quite lucky, but I continued to Work Up and Roost until I got to +6. Luckily, she didn't get any crits. I then proceeded to KO both of her pokemon with Quick Attack.
So I am now at the point when Team Plasma has just stolen the skull. I taught Retaliate to Otto, who I have just withdrawn. I also decide the pokemon that will be boxed this time will be Rose. As I'm not allowed STAB against Burgh, She will be useless as she can only learn STAB moves.
Otto lvl. 17
He's a bit under-levelled, because he has been boxed since Striaton gym. He should be useful now he's back in my team though.
Timothy lvl. 22
Timothy hasn't got the best stats, but should improve once he's evolved. He has quite good moves for this point in the game.
Roman lvl. 21
To be honest, Roman isn't great. He's only on my team because he's a flying type.
Rose lvl. 24 Currently Boxed
Rose was my MVP in that last battle, but she is the pokemon I chose to box until Burgh. She won't last the game in my team, but she has proved herself, until better options come along.