This card has pretty low stats for its cost, having -1 HP from Gyftrot. However, like Gyftrot, Greater Dog has a 2nd ability. This ability allows him to gain +3 HP if you have at least 1 Dog in your hand (including other Greater Dogs), which brings his HP up to 9. This allows it to survive quite a few strong monsters, like RG01 and Undyne.
To activate its Magic, you need to have at least another Dog in your hand. Any is fine, but Doggo works very well due to the fact that if Greater Dog gets weak, you can use Doggo to bring him back and replace it. And due to Doggo's effect, Greater Dog's cost is lowered by 2, making up for the fact that it may not be able to use its Magic again because Doggo left your hand.
This can be countered easily with Penetration by removing its Taunt. It also countered easily with Madjick. Silencing it with Scarf Mouse or Nacarat Jester works also very well, not only removing the Taunt, but also the HP boost.