I never had problems with any fight in Cross (in fact, there wasn't any enemy that took more than half an hour).
But, a puzzle in Trigger... When you are in the Arris Dome... In front of the control panel, you have to hold R+L and then press A. Ha! I couldn't go further, for a month! Why? Because I had to set turbo keys in the emulator, otherwise the contol panel didn't work.