When you go into the Dwarven kings throne room and start talking you will end up fighting a fight with 3 Calca and 3 Brina dolls. If you don't kill all of these very fast they will merge into a large Calcabrina Boss. I highly recommended that you allow this to happen or you will end up missing the first opportunity for a beast entry and this achievement. This fight isn't special and regular fight and heal will get you through it. The fight with Golbez after however is very likely to kill you unless you know what to do. and if you do die on him you will have to face this boss again.
Golbez will kill all party member except Cecil which are saved from the same fate by Rydia. This fight will be tough you have to keep Rydia alive while only attacking with none elementary weapons or Golbez only weakness, which change during the fight. any other element attack will cause Golbez to gain health. Use Libra magic to find out the weakness, in my fights wit him it has always been ice, fire, ice. so make Rydia cast Shiva, then Ifrit and if that wasn't enough Shiva again. Don't waste effort in trying to raise your fallen party members Golbez will kill them again before they get back on their feet. Cecil should heal the party and cast Libra to check the weakness while Rydia will cast the proper magic/summon to take advantage of it.