Instructions
Visit Route 215 or Route 214. Route 215 is to the east of Veilstone City, and Route 214 is directly to the south of Veilstone City.
Run back and forth in the grass on either route. If you do not stay within the grass, you will not encounter any wild Pokemon. Mightyena will eventually appear, although it may take a few attempts, because the chance of finding Mightynea is around 22 percent, according to Pokemon.Marriland.com.
Battle Mightyena with a Pokemon that's within two to three levels of Mightyena's level, so you don't accidentally kill Mightyena with an overpowering attack. Bring Mightyena's health down to about 25 percent, or slightly lower, and then throw a Pokeball. Use a more powerful Pokeball or use a weak attack to lower Mightyena's health, if Mightyena breaks free from the Pokeball.