Instructions
Capture a Bug-, Ghost- or Dark-type Pokemon. These Pokemon have an advantage over Psychic-type Pokemon. Train the Pokemon until it's at least Level 50. Make sure the Pokemon knows Bug-, Ghost- or Dark-type moves that deal damage to the opponent. Battle Dialga or Palkia. After the battle, the three Pixie Pokemon will position themselves at the three lakes.
Purchase 50 to 150 Ultra Balls from a PokeMart. Use "Fly" to travel to Snowpoint City. Head west and you will find Uxie in Lake Acuity. Fight the Uxie with Bug-, Ghost- or Dark-type moves. Throw Ultra balls at the Uxie once its hit points are in the red zone.
Fly to Sunnyshore City and travel west until you reach Lake Valor. Approach Azelf at Lake Valor. Use your Bug-, Ghost- or Dark-type Pokemon to weaken Azelf. Use Ultra Balls on the Uxie until you capture it.
Travel to Twin Leaf Town and go to Route 201. Instead of heading to Sandgem Town, head west onto Lake Verity. Walk up to Mesprit and press "A." Instead of choosing to battle you, it will run off. Check your map from the menu for its location. The map represents Mesprit as a flashing dot.
Get a Pokemon that knows "Mean Look" so that the Mesprit won't be able to run away during battle. Fly to any city and stand near its exit. Walk out of the city and check your map. Each time you change your location, Mesprit will move to a different route. Walk in and out of your city until Mesprit is in the same route as you.
Walk in the long grass once the map shows that the Mesprit is in the same route as you. After a few battles, the Mesprit will show up. Use "Mean Look" on the Mesprit to prevent it from running away during battle. Weaken the Mesprit with Bug-, Ghost- and Dark-type moves. Throw Ultra balls at the Mesprit until you catch it.