To obtain the Cloak of the Midnight Sun you must absorb all the special lids of ice and fire elements in most all realms before reaching the core, and obtain all leader folklore souls. Once you reach the last chapter of the game you will see a video introducing the cloak on Ellen absorbing a memory from the big eye.
Shefra is in Chapter 1 for Ellen. Before Shefra will spawn you must capture every other folk in the level. Once this is complete, go to the middle save point in the level. You will see a turn off to your left; take it. Shefra will be in the back half of the room, but you can't attack her yet. She summons around three or four folks that are a random mix of Ogama and Daru. Defeat these folklore to cause Shefra to resummon them. When she does this, she will lower herself to the ground. Lock on to her and use Cait Sidhe on her. This will take 3-44 hits; keep spamming it. If you get the timing right, you might turn her red before she starts flying overhead. You could try capturing her, and it is possible if you are lucky in the fact that the folks she just summoned stay on the other side of the rocks in the middle of the room. It may be easier to hurry and defeat the folks first. She will stay in that sleep state for around 5 minutes, so hurry and take out the Ogama and Daru, then go back to capture her. Her timing is difficult and will take several tries for most to yank her id. If you're having trouble with the Daru, they can be one-shot with Cait Sidhe. The easiest way to defeat the Ogama is to hit them twice with Boobrie and then do a 4 hit combo with Pouke. To save time when Ogama turns red I just finish him off with Pouke instead of trying to absorb him.
To unlock the Hell Realm Cloak, you must destroy five Memory Stones. The following are the locations of the five stones. Keep in mind that all enemies in a location should be destroyed; otherwise, the stone you seek may not appear:
1.) Hill of Brimstone 1 (I) 2.) Hill of Brimstone 1 (II) 3.) Condemnation Tower (Level 2, East) 4.) Condemnation Tower (Level 3, West) 5.) Hill of Brimstone 2
After all five stones are destroyed, a sixth stone will appear. Head to the Inquisition Bridge to find and destroy it. The Hell Realm Cloak will then be yours.
Check the Netherworld picture books for tips and tricks. They will give you the exact strategy needed to defeat the folk creatures and folklore bosses. In order to get the pages of the Picture Book, be sure to check every room carefully (don't forget you have a map when you press the Select button), defeat all the Folk you come across, and destroy any of the floating crystals that hide treasure.