This mission has a lot of Red Orbs to get - if you know where they are - as well as multiple optional paths to explore.
Walkthrough
Lair of Judgement Ruins
There's a Divinity Statue still standing near you, after you start the mission. Beowulf Devil Arm is located near the place where Vergil fell off into the chasm, and you have to take it and equip at the Divinity Statue. Go to the left-most corridor and walk to the end of it. Double jump and you'll receive a hidden Red Orb cache. After that, go to the other side of the room and break the Combat Adjudicator - blocking the sole exit route - using Beowulf (Combo I - Beast Uppercut - Combo II - Hyper Fist - Killer Bee, repeat). Take the Blue Orb Fragment dropped by it and enter the room.
Underwater Elevator
Run around the lift in front of you and there's a Red Orb crystal behind it. After you've earned the orbs, take the lift to the next area.
Subterranean Lake
It is possible to climb the wreckage near the waterfall and go all the way back to the Sunken Operahouse, but that's the incorrect direction as there is nothing new to find. Instead, go across the pathway directly across from the elevator and enter the broken wall.
Top Obsidian Path
Walk to the end of it, double jump to the wall to receive another hidden Red Orb cache, then go through the door.
Vestibule
Cross the Vestibule area and zone through the hole on your right.
Altar of Evil
Crack on the wall resemble "14", depicting mission's number.
The area will close off until you kill the Dullahans that appear. Enter the unsealed door in the corridor in one of the statues.
Temperance Wagon
Take the large Green Orb in the hidden area beside the Temperance Wagon, board the Wagon, and ride it to the other side. A Hell Vanguard will spawn, along with some other jailers, on the wagon ride. Once everything is dead, you'll arrive at the other side of the railroad. Use the Divinity Statue if you need so, and enter the room to face a puzzle of multi-colored doors and rooms.
Hell's Highway
This room is in fact a dungeon complex, which will lockdown you time after time to force you into battles with the Damned Chessmen. First, head into the green room at the fork, and you must battle two separate sets of Damned Chessmen. Backtrack and go into the purple room to battle a set of Damned Knights, followed by another. Evade roll their ground pound attacks. Go into the green room to collect the Vital Star S. You must pay the price for grabbing it, however, as you must fight three Damned Knights and a few Damned Pawns. Walk into the red room to battle two Damned Knights and a Damned Bishop. Once they have been defeated, go into the purple room and go left through the doors. You must fight several Damned Knights and Bishops to obtain a Blue Orb Fragment. Exit through the last door in the room to finally get out of the puzzle.
If you get lost, just go to every room. Chances are you will battle a few Damned Chessmen and the fight in the last room rewards you with a Blue Orb Fragment, and behind it is the exit.
Subterranean Garden
Now you are in the bisected Subterranean Garden. Jump up onto the sign/pedestal to reveal ANOTHER hidden Red Orb cache. Take the small door in front of the Divinity Statue to find yourself in the familiar area of Subground Water Vein.
Subground Water Vein
Run forward, and you'll see a bright white light column in one of the platforms. There are Enigmas here, but they do not need to be killed to proceed. Walk onto the light pillar and you'll be taken back to Love Planet (from Mission 3).
Optional route: The door at the other end of the area - the one that led to Rounded Pathway - now opens to to the other side of collapsed Top Obsidian Path. This is now a dead end. There are a lot of Damned Chessmen to fight if you wish. A Devil Star lies at the edge of the chasm.
Love Planet
Once again, you have two possible routes here: the way out through the main entrance is the main path, but you can also backtrack into the Bullseye Bar to break stuff for some free Orbs and health, and go back even further if you wish - see below.
Optional route: Once in the bar, head back to Slum Avenue nº66 (Enigmas, and Hell Prides, Lusts and Wraths are lurking in there), then to the Dante's Office Front. You can grab a free Gold Orb/Yellow Orb here. If you want to fight, Hell Sloths, Gluttonies and two Hell Vanguards are waiting for you, but you can just as well ignore them all, run straight back to the bar and resume your progress.
13th Avenue: Aftermath
Collect the Red Orbs from the left-hand building. Grab a Holy Water from the last building on the right. There's another Red Orb cache on the top of the truck sticking out from the building where you collected the Holy Water. Run towards Temen-ni-gru to end the mission.