Location
This Secret Mission is located in Mission 03: Flying Hunter, after completing the second area in the underground tunnels by destroying the Blood Clots and doubling back to the blocked-off door. This leads into a vertical stairwell: drop down to the bottom of this area and walk forwards into the barred-off tunnel to find the red spot on the ground. Rotate the camera a hundred and eighty degrees and point it upwards to find and align the secret mission sigil.
Walkthrough
The goal of this Secret Mission is to kill all seven Red Empusas before any of them are able to escape. Luckily, they do not all spawn in at the same time, rather appearing in groups: the final group of three is the trickiest, and it is important not to allow them to scatter. If a Red Empusa starts to tunnel away, move to it quickly: the escape animation can be interrupted by dealing enough damage to the creature that it rears up on its back legs.
Using multiple Ragtime Devil Breakers is a good idea: by using their Break Age move, all of the Red Empusas will be frozen in place, preventing any of them from escaping. The final group also spawn close enough that Ragtime's basic move will slow all of them, preventing the group from separating.
If the player is returning after completing the game, making copious use of Nero's Charged Shots and Devil Trigger will make this mission much easier.
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