Labyrinth Missions are, like the boss battle in normal missions, instanced areas (where only parties can enter as groups or players by themselves).
Most of the Labyrinths involve two or more parts, where one kills the normal mobs (and occasional mini-boss) and the second part where players face off against the bosses encountered in the normal missions.
In order to recieve a Perfect Clear for the labyrinth, all one has to do is stay alive through the mission, which means using a rebirth rock or simply dying will have the player forfeit the Perfect Clear until they manage to fulfill the requirement.
Some of the labyrinth maps are on the forums and the wiki as well:
All credit for these maps goes to DeadMachine of the GhostX forums.