I found this strategy for that Secret Mission: Strategy: Keep jumping in and out between the two Kyklops to bait them into spewing rocks at each other. Try to linger for *just* long enough to make sure that the rock attack hits the other Kyklop, as, if you jump away immediately, the Kyklop will turn away from its mate to track your position instead. DT whenever you have it. Don't use guns or melee attacks of any kind, as you will automatically fail. Try to stick to the corner with the blue door, as that way you can see both Kyklops. If one or both of them go on a jumping spree, run and jump until it's over (Air Hike is a big help here), then get back to baiting them into spewing rocks at each other again. As soon as one Kyklop has died, collect the blue orb and exit.
But I don't think it's a mandatory Secret Mission. I don't think any of them are really required. And btw you can just exit through a nearby door to bypass Phantom's cat-and-mouse chases, but if you can beat him you get 500 Red Orbs.
And here's to avoid the Secret Mission if it gets too frustrating (perfectly understandable, even I bypassed it at first XD )
Mission 7 begins after Dante has just added the Guiding Light to his item
collection. Your goal is to bring this key to the sun inscription in the
Castellan Bedroom before the Guiding Light drains Dante's life. Slowly, but
surely it is. Start backtracking and head back to the lion head door you came
from. The door is protected by three Sin Scythes that will attack from
behind. They're rather tough; just don't let them hurt Dante, or it'll
shorten the time you have. Must I always tell you to check the Enemies & Boss
Encyclopedia every time there is a new enemy? I guess so. See the Enemies &
Boss Encyclopedia for details on how to scrunch up this bunch. Or you can use
the shotgun and go trigger-happy.
====== OPEN A NEW PATH ======
Strike the dial to activate the elevator and ride it up. Descend back into
the bedroom, then use the Guiding Light in the appropriate place. You end
the mission, but you don't immediately kick into the next mission. Instead,
there's a little intermission that allows you to take your time and complete
some things you've neglected to do before.
You find yourself on an overhang high above the main entrance hall. Jumping
across the gap and going through the other door initiates Mission 8, but you
don't want to do that yet unless you're prepared.
-Also, at the Staircase you can just go through the door to avoid fighting those Marionettes/Bloody Marys. I always end up doing that.
(Taken from https://gamefaqs.gamespot.com/ps2/44510 ... faqs/14361 )
(Secret Mission info taken from https://www.devils-lair.org/dmc1secretmission.php ) -it's just a DMC site, so don't be wary of the site name. lol