Difficulty spike in Three Keys Main Quest

[Laxusthunder]

After beating Abdiel (lv 58), the next main questline teleported you to new Area in order to battle for the three keys right.
I was really shocked to see such high level enemies like Throne (64), Yamata no Orochi (72) and the like while my Nahohino is lv58. My demonic army is even much lower, e.g I currently still use lv 50 Yamato, lv 52 Sakuya, lv 53 black rider. The rest is like lv 40ish Hayataro, King Frost, Alice, Idun lol.

Just wondering if this was the intentional design. Do you guys just push through by grinding for levels, or would you backtrack and did smaller subquests first? Or maybe this required toggling Mitama occurance to "Increase" from the normal rates..I only used it early in the game then reverted to normal rate as it felt too cheesy. Do lemme know :)

[Lynfinity]

Higher-level enemies mostly wander the area leading to Asakusa, the rest of the map contains demons like Hecatoncheires, Queen Medb, Gogmagog, Moirae Sisters and so on. Meaning, the intention is for you to explore the rest of the map, which will naturally bring you up to at least Level 65, and only then head to Asakusa to grab the last key.

[Smugleaf]

Exploring the whole map first and doing the sidequests should be enough to prepare you for the boss fights. It was like that in the original game too, where levels mattered more since it had a significant impact on damage, so it was intended to save the boss fights until the very end.
You don't really need to grind since sidequests give out plenty of EXP and you'd probably be fighting some encounters on the overworld just to recruit more demons.