First, you need to complete the game (defeat that big tree) AND have completed what I believe to be 90 or more missions (according to what Google translates "ミッションクリア数" to be)
Next, you need to get 3 crystals from Satan.
(The 3 greyed out ones):
Next, go to the basement and use the bottom right portal.
Next, find the "深緑の森・D2" map. and with the 3 crystals equipped, talk to the statue after completing the above prerequisites to unlock the last class.
Once you have the last class unlocked, go back to the last dungeon's entrance and deposit these items:
韋駄天の指輪
韋駄天の指輪+
魔導水晶 (auto revive on death item)
After you do this, you'll be able to go into the dungeon.
The dungeon is going to be one of those Dungeon Trials with 101 floors.
Also, 3.3.1 will have an extra bad end if you lose the fight on floor 101.