This boss has only two types of attacks; the fire breath while on land and the fire breath while airborne. Both are very easy to dodge; you just need to keep your eye on the dragon, while regularly switching between lockon and regular camera view. Take note that getting hit by its fire attack will instantly kill you so when you see it fly, run as far as you can. It is vulnerable while breathing fire on land. Melee characters should exploit this vulnerability while maintaining enough stamina for them to run just in case the dragon uses its airborne attack.
Ranged characters should stay at medium range so they can run towards the dragon, past its head to avoid getting killed by the fire. Don't be greedy with your attacks; keep an eye on the dragon's movements and your character's stamina then attack only when needed. You should be able to defeat the ancient dragon and take home a huge amount of souls.