The Legendary Beast’s location will change every time you fly, battle, go into a building, or change routes. This may seem like a hindrance, but you can use it to your advantage. Hop on your bike, pop a Max Repel, and start trekking through the grass. If you haven’t had a hit after about 30 seconds, head into the house. When you come back out, the Legendary Beast’s area of roaming will have changed. Rinse and repeat until it appears before you.
Raikou is an electric Pokemon, so ground types will be strongest against it, while water and flying types will be weak. Entei is a fire Pokemon, so water, ground, and rock types will be strongest against it, while grass, ice, bug, and steel types will be weak. Suicune is a water Pokemon, so grass and electric types will be strong against it, while fire, ground, and rock will be weak.
Sleep or Freeze will also work, but since status effect moves like those are temporary, they’re not the best strategy. Alternatively, you can simply throw an Ultra Ball at it. Your chances are very small here, though, as the Legendary Beast will just probably escape the Pokeball and flee.
Save frequently as you go, because if you accidentally knock out the Legendary Beast, you will not have another opportunity to catch it.
