Instructions
New Game Method
Start a new game with Chimchar as your starting Pokemon. If the Chimchar is orange, restart the DS and begin another game. Shiny Chimchar's have purple skin and hair.
Use the Shiny Chimchar in battles. Once it reaches level 14, it will evolve into a Shiny Monferno.
Battle with your Shiny Monferno until it reaches level 36. At this point, it will evolve into a Shiny Infernape.
Breeding Method
Begin a new game. Choose a Chimchar as your starting Pokemon and fight with it until the Pokemon reaches level 36. It becomes an Infernape at that level.
Go to Jubilife City and enter the Global Trading Station on the Western side of the town.
Enter the station and access the GTS menu. Perform a search for a Pokemon you can breed with your Infernape, such as an Infernape of the opposite sex or a Ditto. This Pokemon must come from a different-language version of the game (either European or Japanese). Perform a trade to get this Pokemon (you will have to give up one of your existing Pokemon to do so).
Go to Solaceon Town and place your Infernape with the creature you just traded for (either the second Infernape or Ditto) in the breeding center. The Pokemon will eventually breed.
Return to the breeding center and get the Pokemon egg. Walk around with the egg until it hatches. If the Chimchar's hair is purple, it is a shiny Chimchar and you can level it up to level 36. If the Chimchar is not shiny, repeat step 4.