Make sure to buff up before fighting Barthandelus. Make sure you use the aegisol buff. Then use your Liba Scope ability in order to understand its weaknesses. Attack the smaller heads before attacking the main upside down head, because in the beginning it will be almost invincible. After attacking the sides of the boss, attack the main head. If your health drops to about half, switch over to medic class and heal. The boss has some strong attacks so make sure to be ready for them. If you buff up and max out your crystarium before fighting it should be an easy battle.