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Enter The Colosseum and talk to the lady. Answer "YES" to all of her questions.
Level 30 Barboach
Level 31 Sandshrew
Can you say "easy"? I suggest trying to purify some of your Shadow Pokémon in these battles.
Level 30 Natu
Level 30 Meditite
Too easy. Next!
Bandana Guy Vilch
Level 30 Electrike
Level 31 Cacnea
Level 32 Vulpix
It's getting tougher, but still no problem.
Level 32 Bagon
Level 32 Goldeen
Level 31 Magnemite
Level 34 Delibird
Your first real challenge in my opinion out of any battle. All 4 Pokémon will take a while to take down. You're likely to lose one or two Pokémon before winning this.
That's the last Colosseum battle. For winning the lady at the counter gives you lots of money and the TM Toxic. Teach it to Umbreon and get rid of Snatch. Save, for you have been automatically healed already.
The Cipher Hideout
Now it's time to enter the Cipher Hideout. Leave the Colosseum and go down the bridge. On the bridge you'll be confronted by a Cipher Peon. He won't battle you but he'll ask you to follow him. You're about to get awarded a Shadow Pokémon when the girl Peon realizes you're the guy who's been giving Miror B. all the trouble. Now the Cipher Peon will battle you.
Cipher Peon Nore
Level 32 Pineco
Level 32 Surskit
Level 31 Nincada
Level 33 Shadow Yanma
Easy. Catching Yanma will be so-so difficulty, and Pineco, Surskit, and Nincada should all be killed in one hit.
Upon defeat, Duking and a few other people appear. You find out this is where Shadow Pokémon are being given to thugs for winning (if you didn't know that already), and that Duking's Plusle has been kidnapped. Now we've got to put a stop to Miror B.'s plans and rescue Plusle.
Leave the building and the city. Head back to Phenac for a very short detour.
Enter the Stadum in the middle of the second floor. Take a sharp left and talk to the lady at the whiteboard. She'll give you a P☆DA upgrade, a Strategy Memo, which is similar to a Pokédex. It gives data on all Pokémon met so far.
Head to Outskirt Stand. By now you should have few Great Balls, so buy as much as you can there. Now head back to Pyrite.
To the right of the bridge is the Cipher Hideout. Enter. Take a right and go through the top-left door. You'll be met by Roller Boy Pike.
Roller Boy Pike
Level 33 Taillow
Level 34 Hoothoot
Use a Pokémon that's good against Flying or just your needing-to-be-purified Shadow Pokémon.
You can now save and heal in the room right below the Roller Boy. Right below the healing machine is a well-hidden Ein File H. We'll learn more about the Ein Files later. Go up the stairs. You'll have no choice but to fight the next guy.
Bandana Guy Beats
Level 31 Larvitar
Level 32 Carvanha
Level 32 Barboach
Just like Mirez from the Colosseum challenge, this is a challenging battle, although you'd think Larvitar, the basic form of a pseudo-legendary, would be harder. You can't go half a hallway until you find yet another Trainer.
Level 33 Remoraid
Level 32 Magnemite
Wouldn't be so easy if he had one or two more Pokémon. Further down the maze is...
Level 31 Electrike
Level 31 Voltorb
Level 32 Doduo
Level 32 Ledyba
Level 31 Swablu
Yuck, at least it gets a little more challenging. Harder than Bandana Guy Beats but easier than Bodybuilder Mirez.
Level 31 Spheal
Level 32 Snorunt
There's a Revive in the next room in the bottom-left corner behind the door before blue-haired Trainer who, surprise, surprise, will battle you without hesitation.
Level 31 Horsea
Level 32 Oddish
Level 32 Sandshrew
Easy. Easy. Easy. When will it stop?
Level 32 Cacnea
Level 33 Tentacool
Apparently not now. You should go downstairs and heal/save anyway. Now you're on the roof when you get back up. Head left, ignoring the grunt, and enter the door. You'll find Silva defeated by two Miror B.Peons. Challenge time!
Miror B.Peon Reath
Level 33 Spinarak
Level 32 Luvdisc
Level 20 Shadow Remoraid
Hey! Finally, a Shadow Pokémon and a challenging battle. Be very careful with Shadow Remoraid. I'd suggest using Umbreon's Toxic and then throwing a ball immediately when it hits yellow. It shouldn't be that hard to catch.
Immediately after defeat, Reath's best friend/sister Ferma challenges you. She's much harder.
Miror B.Peon Ferma
Level 32 Aipom
Level 31 Furret
Level 33 Yanma
Level 33 Shadow Mantine
Mantine should present a challenge in catching, Furret's a beast, and Aipom and Yanma are so-so. After beating her, Silva will ask if you know Duking twice. Answer "YES" both times. Miror B. will show up on the television. He tells them he's been using Plusle as bait to get them to follow him. It's a perfect "tactic".
Ein File S is just there. Go downstairs and enter the elevator. Downstairs are 3 Hyper Potions. You're back in the lobby. Heal+save. Move your party around if you have to. Go back up the maze and you should now talk to the grunt. These guys just don't get it. You defeat their leaders yet they think they can beat you.
Level 33 Goldeen
Level 33 Linoone
Level 33 Shadow Qwilfish
Goldeen and Linoone are so-so difficulty, Qwilfish can be pretty hard to catch. Remember you can catch Shadow Pokémon later at the very end of the game if you have to. He'll now finally let you into Pyrite Cave.