Instructions
Familiarize yourself with the areas in which Pikachu appears in the wild. This varies from game to game, so make sure you know where to look for this Pokemon in your own game. Arm yourself with PokeBalls and, if possible, stronger balls before you head out.
Walk around in the grass in areas where you know Pikachu can be caught in the wild. If it appears at the far end of a particular route, avoid the grass as much as possible to get there. Consider using a Repel item, which prevents lower level wild Pokemon from attacking you, since to catch Pikachu, it must be the first Pokemon you encounter along that route.
Use mild attacks to weaken the Pokemon, and avoid accidentally knocking it out. If you can, put the Pikachu to sleep or use another debilitating attack. Use PokeBalls or stronger Balls to catch Pikachu.
Try again in another route where Pikachu appears in the wild if you encounter another wild Pokemon before Pikachu or are otherwise unable to catch it. Be aware that due to the rules of this challenge, your chances of actually being able to catch Pikachu are rather slim, especially since Pikachu is uncommon or rare in most of the games.