Overall, this is a short mission that requires some thinking.
Walkthrough
Gears of Madness
After you activated the bridge, go to the other door. You'll face some Enigmas.
Before you enter the first door, there is a ledge at the left, jump onto it to obtain a Devil Star. Wall Hike and perform Sky Star towards it (You can also get there with Air Hike. Jump from the ledge out, air hike, then pull back immediately. You should land on the ledge easily).
Now you will stand in an area where there is a red portal. That is the Secret Mission "Hang Ten". This secret mission is pretty easy, but a maxed out DT can be useful. Just run towards the Blue Orb Fragment and ignore enemies.
Go through the door on the lower level.
Altar of Evil Pathway
After you completed the secret mission, you will enter a long corridor. There's a Blue Orb Fragment on the top of the door you just came in. Jump up onto the pipes to reach it. Kill all the Soul Eaters to unlock the door.
Altar of Evil
You will then enter a room with statues lining up on the left and right of the room. Jump up to a side of the room and push a block of cube into a door for both sides. Now you need to kill the enemies in the room. There is a Hell Vanguard and more Soul Eaters.
After that there will be a door opening from one of the statues, this will lead you to the Temperance Wagon.
Temperance Wagon
There's an Agni & Rudra SS Rank Combat Adjudicator under the ladder. Push a statue that stands beside the wagon as far as it will go and stand on top of it for a hidden Red Orb cache. You've pushed it far enough when you attack it and it doesn't move any more. There's also a Holy Water and a Green Orb.
Ride the wagon. You will face a lot of enemies when you're riding the wagon so kill them. The enemies will jump from the second rail onto your car. Some enemies will stay on the second rail: You can target them with you guns by using the R3 button to change lock-on targets.
You will then arrive at the door to the Torture Chamber and a Divinity Statue.
Torture Chamber
Approach the pedestal to trigger a cutscene and a boss fight against Beowulf the Lightbeast.
Boss: Beowulf the Lightbeast
Attacks
Beowulf the Lightbeast's attacks are mostly short-ranged so just keep rolling or dashing. However, be careful, as he deals HIGH DAMAGE if he lands even a single hit on you - no matter on what mode.
- Beowulf Combo I: Instead of the finishing upward kick, he finishes the attack with a hammer punch to the ground. You can easily avoid this by Air Hiking, if you have it. Otherwise, side roll thrice.
- Backhand: When you are standing behind Beowulf, sometimes he turns around quickly and strikes out with a backhand. Run, roll, or dash away to avoid this counterattack.
- Cage Drop: Beowulf stomps repeatedly to cause metal cages to drop from the ceiling, and will then attempt to throw them at Dante. Side roll or dash to avoid them. If your timing is good, you can destroy them with various attacks (e.g. Helm Breaker or Aerial Cross) for Red or Green Orbs. Level 2 Swordmaster for Sword Pierce will also do this, and if timed correctly can do a significant damage to Beowulf as well, by hurling the cage at him before he punches it. If you position yourself well, you may find a space where Beowulf cannot hit you with the punches, allowing you to beat on him freely during this "phase" - but it is tricky to pull off this maneuver.
- Stomp Attack: Later during the fight, Beowulf will try to stomp you outright, instead of relying on the cages. Side roll to evade, and watch out for more cages coming your way (they tend to drop near Beowulf's position).
- Bull Rush: He will drop to all fours and run from one side of the battlefield to the other, attempting to trample Dante. He will change directions three or more times in one bout, each time targeting Dante. Side-rolling out of the way can be difficult, but jumping over him with Air Hike or Sky Star is generally safer. You can also run away, using Devil Trigger sprint ability.
- Body Slam: Usually after a series of failed rush attacks, Beowulf will end by attempting to belly flop on top of Dante. Jumping over this attack can be difficult unless you have Air Hike and start jumping as soon as he does, but he may still catch you. However, this attack is easier to evade by rolling than the run attack.
- Feather Barrage: The most difficult attack to evade. If you stay too far for too long, Beowulf will counter by opening his wings (shouting "SPARDA!!") and launching his light feathers at Dante. The feathers act like homing missiles, and will inflict big damage if they catch you. Just running away or dodging isn't sufficient to avoid this: try running from the first few volleys and dodging the last one with a roll or jump. However the safest way to avoid that is to get behind him, but it only works if you are very close (keep running towards Beowulf's back).
- 'Volcano: Beowulf slams his right fist into the ground, causing a large light burst to erupt. VERY dangerous attack, causing high damage and covering a lot of space. Don't jump, as the burst also reaches into the air. Running away is the easiest method. Beware, as Volcano will cause nearby standing cages to be hurled in the process, straight away from the Volcano. To avoid these cages, stay out of the diameter line detemined by Volcanos epicenter and the cage's position.
- Wings of Light: Beowulf says "I will KILL YOU!!", then spreads out his wings, creating a blasting sphere of light. Do anything to get away, but the most effective method is to jump away. Air Hike is a good solution. The first time Beowulf executes Wings of Light signifies that he had entered berserk state.
- Eye Blast: Very rarely, if you stay in the air in front of him for some time, Beowulf might attempt to use his intact eye to attack you. This attack is easily avoidable since it will damage you only if you remain directly in front of his head.
Initially, Beowulf will rely on his three-hit combo (Beowulf Combo I). Once he reaches about 2/3 of health, he will stagger (either by flinching back, or kneeling and clutching his eye) and enter a berserk state. This is represented by him shouting, "I will KILL YOU!!", his eye will also flash in red, and a white Devil Trigger-like aura will surround him, damaging Dante or Vergil if they are too close to him (Wings of Light attack). He will then do a Bull Rush to one of the corners of the chamber, and do a single Cage Drop round (about 4 cages). Afterwards, he will resume his assault. All of his attacks will now become stronger and faster - as well as more varied - and he will also attack more frequently. He may stagger and do the Wings of Light again at about 1/3 of health left, after which he will become even more aggressive - in particular, he will execute Stomp Attack and Volcano more often.
Strategy
First playthrough
Beowulf is difficult to fight because he's not vulnerable for very long, and he will only increase his aggressiveness as the fight progresses. Always blind Beowulf because his eye is sensitive and will double your damage done to him. Use an aerial attack (Aerial Cross recommended) on his right eye to stun him, but watch out for his counterattack. The safest place to be as he's flailing is just to the side of his left ankle. The best way to fight him is to chip away at his health with firearms when you can, and slash at his eye when he tries a Beowulf Combo I on you. There's no particular Devil Arm to kill Beowulf faster, just use your best weapon. Prop Shredder will stagger him, if used directly after or during Beowulf Combo I. Make sure you are standing directly in front of him when you do it though.
Second playthrough
The strategy is very similar to the first time. Kalina Ann is a good ranged weapon in this mission if you have it. If you're really good with Royal Guard, Just Guard the Beowulf Combo I. That way, you can gain "Anger" orbs quickly, as shown on the Royal Guard Meter. When he uses Wings of Light, Devil Trigger Explosion and Aerial Just Release right next to him (aim at the head), to deal massive damage to him. This is especially helpful on Dante Must Die mode. You can also do the same by baiting him into Eye Blast. If he tries to get you with Feather Barrage, use Ultimate (Royal Guard Level 3) to nullify it.
For Vergil
Use Yamato, since it bears the element of darkness, which counters Beowulf's element of light (this is signified by the dark aura generated by Yamato when it slashes Beowulf). Simply use Yamato Aerial Rave on his eye, then Trick Down to safely avoid his "flail" attack. You can use Judgement Cut against the Cage Drop phase. When he drops on all fours and attempts to Bull Rush you, timed Air Tricks can easily dodge his charges, and even the Body Slam attack, placing you behind Beowulf. Repeat for as long as he charges, then strike from behind when he's finished. If you are trying to finish him off Vergil style (meaning: not jumping but using Trick Up, not running but using Air Trick, finishing Yamato combos either by letting Vergil seathe his sword or Tricking Down/Up), lock onto him and keep locked on. Multiple Trick Downs can avoid the whole Beowulf Combo I, while a double Trick Down, if fast enough can avoid the Volcano slam as well. Use a combination of tricks to avoid the Feather Barrage if you are too far to get behind him.