Note: The time of day is night, so that I can use Dusk Balls effectively
So I have seen a lot of people asking how to catch Raikou and Entei. I have come up with an easy way that just requires a little patience. You need a Pokemon with Mean Look. (False Swipe and Baton Pass are helpful too) You keep going back and forth between routes, checking the Pokegear to see the location of the Dogs/Beasts/Cats. (Whatever you prefer) When one of them is on the same route as you, go into the grass and find it. I have a level 42 Absol that I used for this. It is faster than both Entei and Raikou so I was able to use Mean Look before it fled. Then you would use False swipe to weaken it. (False Swipe will always leave 1 HP left) However if you use Mean Look, they can still use Roar and end the battle immediately. To fix this, you can use Mean Look, then use Baton Pass (Baton Pass keeps the effects of Mean Look going even when the Pokemon is switched out. So you can switch to a Pokemon that has the ability Sound Proof such as Exploud and that will prevent Roar from working. If you would like an Absol with Baton Pass and Mean Look, I am willing to breed mine and trade the eggs. Those two moves will be passed on to the baby.