Dante starts out in a corridor area where it is easy to get turned around. At the first fork in the path, go right to encounter the first sealed-room battle with a Nobody and find the Blue Orb. Picking this up does not result in the mission ending, so grab it and head right again to encounter a second Nobody, then right again to encounter a third. Once this one is defeated, slash though the green membrane to enter the second area of the mission.
This area has a cracked floor with lava visible though it, though unlike the pools of lava in Mission 21 itself, this floor does not deal damage to Dante. Directly ahead, the pink structure with a swirling red seal around it acts as a Red Orb Fountain, so smash it before proceeding upwards.
Up here Dante will encounter the same "Pluto's Dragon" enemy seen in Mission 17. This time rather than spitting fireballs like Phantom, it unleashes a flamethrower attack similar to that of a Fetish at regular intervals. Dante has to defeat this one with direct damage: it is immune to firearms, so use melee attacks and back off when it breathes fire.
Once it is defeated, a pair of Frosts (four on higher difficulties, a maximum of two at a time, with the first two on a 15-second DT timer in Dante Must Die mode) will spawn in the area below. Jumping down and defeating them will trigger a cutscene showing some floating eyeball platforms appearing in the upper part of the room. Climb up to them and use the first two. Ignore the third, and proceed to the right to find an alcove containing an altar-like structure with an item on it. This is the Bangle of Time: pick it up to finish the secret mission.
Alternatively, it is possible to reach the Bangle without fighting the "Dragon" by climbing up to where the first eyeball platform would appear. From here use Air Hike or kick-jump off the wall, then activate Air Raid. Fly to the platform near where the second eyeball platform would appear, land, then jump off it and use Air Raid again to fly across to the platform with the Bangle.