Instructions
Obtain the National Pokedex. You will first have to defeat the Elite Four and complete the Sinnoh Pokedex. You complete the Sinnoh Pokedex by catching sight of all 150 Pokemon in the Pokedex. Once you have completed these two tasks, go to Professor Rowan in Sandgem Town. He will examine the Pokedex, then Professor Oak will come in and give you the National Pokedex.
Go to your rival's house (either Lucas or Dawn) in Sandgem Town and talk to Professor Rowan's kid sister. She will tell you about a Swarm that is taking place on a certain route or specific area. The location changes every day. If you go to the location she specifies, you can catch certain Pokemon that are not found elsewhere in the game. Visit the girl every day until she tells you about a Swarm on Route 222.
Go to Route 222, which is between Valor Lakefront and Sunnyshore City.
Begin battling Pokemon on the route until you encounter Skitty. Use a Pokeball to capture the Pokemon.