After making your way through Miroir Way east of Geosenge Town, you reach Reflection Cave on the way to Shalour City.
Battle and Catch
In the cave, you may randomly encounter Mr. Mime, Wobbuffet, Sableye, Chingling, Roggenrola, Solosis, and Carbink. In addition, you might have horde encounters with Mime Jr., Roggenrola, or Carbink. Be careful of shadows from the ceiling because if you walk under them, a Woobat or Ferroseed will fall from above and attack you.
Just inside the cave, you find a big reflective wall. Backpacker Lane is staring at it. He sends out a level 26 Linoone.
To the east, the path splits. First, go north to find a Nest Ball.
Go south to where the path splits. Then go east along the narrow path above the rocks. At the end, you find a Revive.
Go west, then south. There is a path going east, but it's a dead end, so just keep going south. You will encounter Battle Girl Hedvig. She has a level 25 Throh and a level 26 Hawlucha.
Go south from the Battle Girl and down some stairs, then take the north path. At the end, go up the stairs to get a Moon Stone.
Go back up to where the Battle Girl is running around, then go east. Ace Trainer Monique will challenge you when you walk past the mirror. She has a level 24 Doduo, a level 25 Helioptile, and a level 24 Granbull.
East of the Ace Trainer at the mirror, the north path is a dead end, so go east and down the stairs to the next floor.
Reflection Cave B1F
The girl in green near the stairs will heal up your pokémon for free.
Continue east. The girl in orange nearby is Tourist Monami. She has a level 26 Nidorina. You get 1872 Pokédollars for winning.
Go east from the Tourist, then north along the wall. When you reach the mirror, go up the stairs (you can see them in the mirror) and go up the second set of stairs to get a Black Belt. If a pokémon holds the Black Belt, its Fighting-type attacks will be stronger.
Go back and walk south from the tourist. You'll run into Tierno, who tells you that using the move Flash will reduce the number of wild pokémon you run into. He gives you TM70 Flash.
Go east from Tierno. There are some stairs that you can see in the mirror, so go up, then go to the right and pick up the Escape Rope.
Go west from where you got the Escape Rope, then south and down the stairs. Up ahead, you run into Black Belt Igor. He has a level 28 Sawk.
Go east and north. When you walk past, Psychic Franz will battle you. He has a level 24 Chimecho and a level 24 Golett.
To the north, you run into Tourist Haruto. He has a level 26 Nidorino.
Go north from the tourist and go up to the mirror to the north. Go east along the narrow path to get a Hyper Potion.
Go west and you will have to have a double battle with Honeymooners Yuu & Ami. They send out a level 26 Vespiquen and level 26 Combee.
West from the honeymooners, you find Ace Trainer Emil. He sends out a level 26 Absol and a level 25 Pinsir.
If you go directly south from the Ace Trainer, there is a slope that gives you a shortcut back to Route 11. If you instead go southwest from the Ace Trainer, there are some stairs going down to B2F.
Reflection Cave B2F
Go north until you reach a mirror wall, then go east and up the stairs that you can see in the mirror. Go down the stairs to the south to get an Earth Plate.
Now go north again to the mirror wall, then go west. Look at the mirror to see a cave entrance in the wall below you. Go into it. You find TM74 Gyro Ball. Go south to exit this room.
Go east, hop off of the ledge, then continue east to go upstairs.
Reflection Cave B1F part 2
Go east from the stairs, then north. Go west from the Ace Trainer to get an Iron. Then continue west and go up the stairs.
Reflection Cave 1F part 2
Near the steps, you find Hiker Dunstan. He has a level 22 Sandile, a level 23 Dwebble, and a level 24 Diggersby.
South of the hiker, there is a stone that you can push with Strength, giving you a shortcut to the cave entrance that goes to Route 11. The researcher to the west of the hiker says that there is another Reveal Glass, which is an item that can transform Landorus, Thundurus, and Tornadus into their original forms.
Exit the cave and you will be in Shalour City.