I will admit to not having all my characters up that high for the master quest map. (I'm almost done with the Termina map and some of my characters are still in the 50s and I have all the weapons/costumes up until now...) It really depends on how you use the characters' movesets. You can get away with not being highly leveled but it seriously depends on how well you play, how well you manage your fairies, and taking advantage of those multi-character levels when you run into them.
The thing is, a lot of rewards require you to A-rank missions. And the problem with that is you can only get hit a very small number of times before you've lost your chance. Even with your badges maxed out, you're going to have a lot of trouble if you get hit a lot.
That said, by the time you hit the Termina map it is a LOT harder. Enemies hit very, VERY hard. There are ways to manage it, but I'm pretty much leveling my lower characters with rupees as they are needed. Also, if you just need a break from running in circles around enemies trying not to get hit, clear some streetpass or "network link" levels. They will drop your highest available ranking gear and materials you can either use them to take a break and play your desired characters without worrying, or level up your lowbies.