cresselia

To catch Cressailia you need to have a Pokemon with shadow tag (or similar ability to stop it from fleeing) and have baton pass, we'll now call this Pokemon "pokemon 1". What you do is hav Pokemon 1 at the front, then as your first move use baton pass to a Pokemon with false swipes. Now, because you used baton pass to switch out you don't lose the ability shadow tag (or other ability). So then you just use false swipe until cressailia has one life left then use a dusk ball if it at night, a timer ball if it has taken more than 30 turns or an ultra ball if you do not fill either criteria. To make it easier you can freeze, paralyze or put cressailia to sleep.

First of all, I highly suggest you get a Haunter or Gengar. You can get a Haunter by trading with a girl in Snowpoint City; you need to trade a Medicham for Haunter. Level him up to his high 40s. Now, teach him Mean Look, Hypnosis, Shadow Ball, Dark Pulse. Some of these moves may require re-teaching him old moves, by visiting the Move Tutor in Pastoria City and trading in some Heart Scales, which you can find Underground. Now, buy about 30 Dusk Balls. Save your game and make sure it's night in-game. Track Cresselia down using the Marking Map on your Poketch, and get into battle with her. Use Mean Look, then Hypnosis. Then, wither down her HP using Shadow Ball and Dark Pulse. If she wakes up, use Hypnosis right away. If she faints, re-start your game and start all over. However, if Haunter gets weak, healing him is your top priority, because if Haunter faints, Cresselia can run away. Once she's asleep and her HP is in the red zone, start chucking Dusk Balls at her, and you should eventually catch her.

I recomend getting a goldbat..most goldbats no's the move mean eye so it can't escape.If posible then go and teach goldbat hynosis.Then easly lower cresselias hp and catch it.