It is highly recommended you know as much about the game as you can, seeing as how one mistake can cause the loss of one or all your current battling Adepts. It is also recommended that you level up as fast as you can and as high as you can. It is also highly advised you enter a Password in this mode in particular so that the power of the original Golden Sun party is noticeably higher than it would ordinarily be, and allows access to all the Djinn. Boss battles, in particular, will be sharply more challenging. Interestingly enough, the only two enemies that do NOT get as significant a challenge boost as others in Hard Mode are Dullahan, the strongest optional superboss (The maximum amount of HP the game's code allows any enemy to have is 16,383 and, because Dullahan ordinarily has 16,000 HP, this restriction keeps his HP from being increased as dramatically as it is for other monsters.), and Valukar (for similar reasons). It is also worth noting that any monster spawned mid-battle (such as the balls Star Magician summons) will retain their original normal-mode stats, and thus will be significantly easier than their Hard Mode counterparts.
Hard mode exists only for optional challenge value, as there are no extra rewards for playing through or completing it.