I dont know where you guys are in the game, but the further you level up, the less you will get tired... I'm at lvl 78 now, and I don't think I've had anybody get tired in the last 20-30 levels(levels not floors)

It is correct that as you level up it takes longer for you to get Tired...

Earlier in the game is a good idea to wait until the last day before the full moon to go to Tartarus, since in the day before the full moon you don't get tired and you can accomplish all requests and level up i just one day....

I believe tiredness depends on the time you have spent on Tartarus. Ive been abusing the Armageddon,Victory Cry skills so my other chars dont really have to do anything but still they get tired. Using escape route while a character is dead will make it tired though and will return to the dorm

I manage to reach the barrier (lvl 15) at 04/25 (2nd Tartarus visit)

Is that good enough?

I have to train my character at lvl 13-15 until the barrier is down

But that is long!

It's good enough, yes, it's even a few days early. The barrier won't be down until May 10, so train around, do requests, and work on your stats.