Sounds like you need better monsters, or at least a good Sentinel. Having a good Sentinel is key throughout FF XIII-2. I recommend getting a Pulsework Knight, which you can get from Bresha Ruins -5 AF-. They're Early Peakers, so they're easy to max out, and they're more than good enough Sentinels to carry you throughout the entire story.
Also, grind a little. That never hurts, and grinding in this game is incredibly quick and easy. Even easy fights give you plenty of CP. I had no problems with my first run through that area or the Faeryl fight, but I had also been taking my time and exploring up to that point, so I was probably a little overpowered. Just grind a little and get a Pulsework Knight.