First off, do not kick the dogs. I tried it for awhile, and there's so many times you get blown up by another dog right after you finish kicking one, so it's too luck based for a fight you can't risk getting hit. I personally had maxed out cestus, so I stayed close and pounded its face in. If you start it back a little, you lunge into the face and kill nearby dogs, but you still need to dodge attacks. The good thing about being this close means the dogs that blow up near you are easily dodged and end up hurting the cerberus. You should start to be able to consistently beat the first heard without getting hit, and the second isn't much different aside from the satyr, which is pretty easy if you can put some orbs in the claws of hades. Also, don't use magic for the first head at all.
Set the Gorgon as the soul summon for the claws. If it isn't there you need to get to..level 3 I think, so hopefully you either have that already or atleast have the orbs. You can ONLY use this magic twice on a full bar though, so you need to be careful. Get the satyr when it's recovering from an attack then smash it like nothing. Then just repeat like the first head and cut off head 2. Now the wonderful part...
For the 2 satyrs, if the planets align and the gods want you to excel in life, you will be able to get both in the gorgon's stare. I never was able to get that lucky, but you need atleast one out of the picture. After this you have a chunk of magic, but not big enough for another summon, so I used the blade of exile's magic by the cerberus here. Then be slow, air dash around if needed and only hit the dog with 1-2 hit cestus light attacks while it throws up pups. After it does, run around and basically just get the satyr away from you. Soon the dog will have the prompt, do it, kill it, relish the moment and the fact that if you're almost dead you'll get more health, then spam throws on the last satyr to easily beat it.