I. Floors:

Advanced Awakening Stones begin dropping from Dimensional Space Floor 5. The increased difficulty simply comes from higher stats, so there's no need to change your strategy. You will face a single boss, and all you have to do is eliminate it. Pay some attention to the boss's imprisonment and stun skills.

Boss Skills:

Heavy Grinder: Deals 100% damage to 1 enemy (The boss' basic attack).

Imprisonment: The boss' main crowd control. It imprisons 1 enemy for 2 rounds. Try to avoid getting your main damage dealer or healer affected by this skill, or you might have a hard time completing the requirements.

Black Hole: The boss' AoE skill. It will grant an extra move if it kills an enemy. To counter this skill, you need to watch all your Saints' HP closely. You'd be at a disadvantage if the boss receives additional moves.

Oblivion: The boss summons Saints and receives skill buffs at certain HP levels. You should try to focus down the boss as soon as possible, since it becomes  dangerous when it transforms.

II. Strategy:

There is a single boss in this instance. Kill it to clear the floor. You will need Saints with strong single-target attacks. Victory Conditions:

Have a certain amount of remaining HP. There is no limit to the number of rounds, so it works as a test of your survivability. It's easiest when you bring a healer. If you have low damage output, you can just chip away at the boss and it'll die eventually. For the healer, it's recommended to choose Eagle Marin, whom you get as a reward for completing the main story. (Bringing Daidalos is also a good choice as he limits the boss' damage)

The boss summons monsters to aid it in battle when it reaches certain HP levels. Even so, continue focusing the boss down to prevent it from summoning more.

III. Recommended Level:

It's recommended to use Saints of at least level 30. They need to have enough HP to ensure that you do not end up with more than 3 dead Saints, which will make you fail the floor.