Sometimes I see Eddie in fights and I just have no clue how to deal with him. He has 10 power (with bonus) which is pretty much impossible to pill against him and he has a powerful healing ability. He's one of the most annoying cards to face. I know that an SOA would probably be the best way to deal with the card, but I don't always draw an SOA.
What's the best way to deal with him if you don't have an SOA?
As the others have already said, it depends on what you have. more importantly it depends on what your opponent has.
Assume low pill. Use a low dmg/gap card with +/- power/atk cards. If he bluffs/minimal pillz you get your dmg through for minimal pillz. If he gets through, you play accordingly.
My decks usually have + life in it, so even if I don't SoA him and he gets through, I can still stay above his life gaining gap with + life of my own.