Entei

I would reccommed using your partner Pokemon or captured Pokemon to help. Also I would reccommed going slowly so you can easily monever around the fire and so you don't hit entei.

For raikou, you can use a ghost poke assist, for suicune make sure you have full discharge.Wait until the 3 suicune get ready to attack then use discharge if they are in the middle.then quickly circle them.Also the one with the shadow under it is the real one. Last is Entei. It took me like 50,000 trys TO CATCH THAT THING!!! Ok,when it has 3 flames coming out of the ground circle it 2 times. That gets rid of 2 of the flames around it.wiat til the flames inthe ground are gone then when he is about to attack circle him. Keep doing that until the numbers on his head appear then do a full discharge when he`s inside of the globe thingy.then circle him very quickly but don't let him break out. Also I reccomend that you have a raichu with you. Bring 2 gastly,donphan and a medicham. Then use the medichamand circle him then boom. You cought Entei.

I would reccommend trying to get a water Pokemon and use him to capture entei.

I was stumped too at first but I found a way, just in case you have trouble with the other two, catch flareon for raikou(wait for the bolts to stop), Use plusle/ minun for the suicune, and use vaporeon for entei. P.s.: for entei, immedeantly after you engage the battle with it, activate the poke assist for vaporeon.