Well, what I do is when I get to a new dungeon, I walk around exploring/leveling up until either I finish the dungeon or one of my characters dies. Then I get out, heal up, and come back.
This way I'm several dungeons ahead of what I am recommended to be at at my level in most walkthroughs. But that is only my second playthrough. So, If PS2 isn't diffucult for you, IMO, it's because of your levels. Picture me around level 15 doing the Green dam.

. Of course, however, I did level up a bit before I did Nei.