Well, there are a few reasons why this might be. Firstly, have you levelled up enough? Seen as it's your second time through, you might have rushed through certain areas as you already knew the exit, and wanted to move on with the story - thus not levelling up as much as you did the first time. If this is the case then I recommend, as tedious as it may be, spending sometime levelling up in the area you're in.

Another reason, only really feasible if you selected the advanced sphere grid, is that you sent characters off their default path - for example you decided to make Tidus a white mage - which left the party unbalanced and weak in some areas. A solution for this is to find out the weaknesses, say a lack of Time Magic, i.e. Haste, and sort out a way to rectify this, by perhaps having a member divert from their path to learn the necessary abilities. You'll need to spend some time levelling up to do this, but it would help.

A further problem could be that you only had select members partaking in battle i.e you only used Yuna when you needed to heal etc. This would have left some characters less developed than others. Make sure that every character takes at least one turn in battle - re-equpping a weapon or armour mid-battle counts, and it has extremely fast recovery time. Also, make sure Yuna levels up as her aeons are very important.

If none of this helps then www.gamefaqs.com/ has some very good strategy guides which should help you.