Persona 3 Bonus Dungeon (Sorry)

Is it possible to unlock the Bonus Dungeon of Persona 3: FES on your first playthrough, or do you have to replay the game in order to unlock it? 
 
Also, i apologize for posting this in General Discussion, but i could only find Persona 4 forum, and not 3.

You mean Monad, the basement? Accept the quest from Elizabeth to beat the Reaper and you can go there on your first playthrough. You can't fight the secret boss in Monad though until you're on a new game plus.

Thanks a lot!

Very important to realize: You must accept the quest from elizabeth before fighting the reaper. Otherwise you will not get the key.

Yeah, i figured. I do all of her quests :D. Thanks again.

You never want to split your party down there, even if you're stacked. I did that with my lv99 characters in P3P, not a good idea.

Lol, yeah i read the dungeon is hella hard, but it's easy to get level 99 in it. Thanks for the advice.