That's a really good question! I was fairly young still when I got my Playstation 1, so I do remember struggling with quite a few games, especially when I was getting used to the controller. I would say one of the games that had me beating my head against a wall though would have been Chrono Cross. I did eventually beat the game, but it took me a long time. I actually had a hard time doing a lot of the "quests" in that game. I remember one of the first things I had to do was jump on those komodo dragons I think they were called to get their rainbow scales. It took me forever to find out how to get all three, and when I finally did get them it was smooth sailing up until I got past the mansion and had to find the Hydra. I did not realize I had to go to the beach to change what "time" I was in, so I just wandered around aimlessly going to every area I could on the main land trying my best to figure out a way into the marshes. I actually think I reset the game a few times in hopes I had done something wrong and glitched the game.
Needless to say, even after I figured out how to time travel (100% by accident!) the game itself still took a while to beat. Between challenging boss fights, a different style of combat I have yet to really see in any other game, and the sometimes misleading or hard to understand dialog (for the age I was), that was probably one of the most challenging games I had played up until that point on the PS1. Of course when I replay it now I look back and wonder how on earth I thought it was so difficult to start with. (Aside for some of the battles, those can still be challenging if you don't allocate your abilities/items correctly).