Instructions
Choose a Catcher Pokemon. This Pokemon should be able to learn False Swipe by leveling up. Scyther and Paras are two such Pokemon. Get the Power Belt (Defense) and the Power Anklet (Speed) at the shop in Battle Park.
Give the Catcher Pokemon the Power Belt. The Power Belt doubles the amount of Defense Effort Values a Pokemon gets after winning a battle. Use the Catcher Pokemon to defeat 25 Onix or Steelix at Iron Island Cave to gain 100 Defense EVs. These will increase the Catcher Pokemon's Defense stat.
Take the Power Belt and give the Catcher Pokemon a Power Anklet. This item doubles the amount of Speed EVs your Catcher Pokemon will get after beating a Pokemon. Go to the Trophy Garden and fight 39 Pikachu and Staravia to get 155 Speed Effort Values. The Speed EVs will improve the Catcher Pokemon's Speed stat.
Train the Catcher Pokemon until it learns False Swipe. This move will weaken a Pokemon until it has one hitpoint. The less hitpoints a Pokemon has, the easier it is to catch.
Collect Rare Candies and give them to your Catcher Pokemon until it's level 100, at which time it will fare well against most Legendary Pokemon.