One concept which I always thought was interesting was the sort of 'Mirror Boss' idea. Like a Boss which compared to most bosses is actually very weak, and could be taken out in four or five turns if they were the kind to just sit there and take your nuking...but they're a party of 3/4/whatever size your party is. One of them would have an AI which loves to buff and acts as a healer whenever someone's HP is low who's semi-fragile, one of them is a strong physical attacker with some minor healing ability and a ton of HP, one is a strong magical attacker, and the other is an incredibly nasty physical attacker who's only got moderate health, but inflicts all sorts of crazy debuffs on your party.
To make it even nastier, you can make the AI as Player-Like as possible, raise their stats or give them new skills if the player's above a certain level and even do some horrible tricks like giving them an inventory and access to healing, and even reviving items that all of them can use.
Although in doing so you could give the player some concessions too; weakening them if the player's level is low, giving them an inventory of a specified size, giving them limited(And truly limited, not a level of which they'll NEVER run out) of SP and forcing them to use their limited SP healing items to restore their SP and continue to assault you, as well as being HIGHLY succeptible to status effects.
Bosses which are strong because they possess the player's strengths are fun; there's countless examples. And having such bosses having the same weaknesses as players could make it interesting as the player continues to fight them until they realize that they can fight using a strategy similar to one they'd use against themselves.