Hard, but NOT impossible!
The battle against Eggman is very, very difficult. However, after about 5 tries I have found out how to beat him.
Start off by using "Protect" IMMEDIATELY. I know it sometimes seems like it doesn't work, but it does.
Next, attack normally until the emerald is exposed, and use Triple Shot when he is charging. You have enough energy to use 3 G-Beams, however ONLY USE 1, IF ANY. They do a lot of damage, but drain your EP like a bitch.
Continue using normal attacks and Triple Shots as stated above, and heal when necessary (ie. you have 1500 HP or less). Once Eggman is down to about 4000 HP, you will probably be out of Triple Shots, but should still have a decent amount of MP. You should now use 1 Purple Vortex while he is charging, in addition to a normal attack. After getting hit, heal up, then once he is exposed again, use another Purple Vortex. Eggman should be more or less dead by this point.
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Now for the review. I really like this series and can't wait for the next installment. I must say though that this isn't a true RPG, only because you can't work at your own pace. Really, the game guides you, and you simply decide the strategy of the battles.
However, despite not being a true-blue RPG, this is definately a fun series. Keep it up!