[This guide contains spoilers] This guide will help you to get through Julius mode and beat this mode of Dawn of Sorrow and unlock the achievement “A Promise Fulfilled” (clear Julius mode).
When I first played Julius mode, I was confused about how to actually beat it, so I created a guide on how to recruit Yoko and Alucard in order to find Soma and end his reign of chaos.
Take in consideration that English is not my first language, so this guide may have some grammatical errors.
TL;DR
-In the Lost Village, recruit Yoko. Then in the Demon Guest House recruit Alucard. Defeat Agoni in the Pinnacle. Head to the Mine of Judgement, defeat Death. Enter the abyss, and where you would find Menace there will be Soma. Marked on the map are the necessary bosses in order:
After defeating Dario (“2″ in the map) don’t forget to go up and left to unlock Alucard so you can pass trough the” puppet master required” walls with the bat form.
How to unlock Julius Mode
To unlock Julius mode you have to get the good ending or the “second bad ending” on normal mode (aka Soma mode). This bad ending is the one you get if you meet Celia in the Garden of Madness without the Mina’s Talisman equipped. As a reminder, in order to get there you must have to defeat Agoni, Darío’s inner demon beforehand. You unlock that bossfight using the Paranoia soul on the Dario bossfight on the Pinnacle. You can search a normal mode guide if you don’t know how to obtain these souls.
So, you will unlock the bad ending by just entering the room; this will trigger a cutscene and after that the game will save and you will unlock Julius mode.
After that, you must use a empty save file to start a new game in Julius mode.
The most notorious changes are that there are 3 playable characters (Julius, Yoko and Alucard), and the fact that pressing start will simply pause the game. This is mainly because in Julius mode you can’t change loadout (souls, weapons, armor, etc.). To compensate this, Julius (and friends) will have different set of skills to go through the castle from the beginning:
Julius will attack with his Whip, a little upwards dash, can break ice and can use different special weapons like they were red souls for Soma. These are: Axe, Holy Water, Boomerang and a special Holy Cross attack. The first three will use a small amount of MP and the Holy Cross will channel and use a lot of MP. You can loop through these with the right bumper on controller.
Yoko will use a club that deals low damage but heals you with each hit. She can’t dash upwards, but has a really long back dash. She has three spells that can be used the same way as Soma’s red souls. These are: Ice spell, Fire spell and Lightning spell. The first two will use a small amount of MP and lightning a lot. You will find Yoko here, where she usually is in normal mode:
Finally, Alucard will use a sword, has a really long upwards dash and CAN’T SLIDE. He has 2 abilities that are also used like Soma’s red souls: Fireballs and Bat mode. Fireballs uses a small amount of MP and bat mode just consumes MP slowly. You can find Allucard here: 
Once unlocked, you can loop through them with the Y button on an Xbox controller.
Walkthrough
Starting a new game of Julius mode will find you at the start of the castle at level 1. You will deal a decent amount of damage, so I recommend fighting Flying Armor from the start. So, after crossing the second bridge drop at the intersection, go right to save the game and fight Flying Armor on the left. You won’t need to seal the boss. After that, go where Yoko usually is in normal mode and she will join your party.
After that, I recommend heading east to enter the Wizardly Lab, and then enter into the Garden of Madness. You can do so by breaking the ice with Julius while standing on the moving platform[imgur.com]
After that, go up and find your way to Darío boss fight. You can go either right or left. 
After defeating him, go up, then left until you find Alucard. He will join your party. You will find him in this room:
Now you should go back to the Garden of Madness and head to the Dark Chapel on the right. With Alucard in Bat mode, you can pass through the puppet master wall.
Now you can continue to Gergoth boss, at the top of the Condemned Tower. This boss can be hard. Use the rewind option if needed. After defeating it, reach the top again to grab the tower key and enter the Cursed Clock Tower. Remember that Alucard can perform a really high upwards dash that may save you time.
In the Cursed Clock Tower, go left, then up to find and defeat Zephyr.
Now, you can access to the Pinnacle. This zone is hard, so I recommend avoid getting hit too much. Reach the top and you will fight Agoni.
Defeat Agoni and the door leading to the Mine of Judgement will open. Now, we find our way there.
At the bottom, you will fight Death. This is without a doubt the hardest one in Julius Mode. Deals a ton of damage and is difficult to dodge. I recommend learning his attacks and using the rewind function if needed.
At the end of the Abyss, you can cross the door to fight Soma.
Good Luck and enjoy the fight. Defeating him will unlock the achievement “A Promise Fulfilled”.
Acknowledgments
I would also like to thank Sabberzombie for this FAQ they made some time ago that I used as reference: https://gamefaqs.gamespot.com/ds/922145-castlevania-dawn-of-sorrow/faqs/71997
If there’s something that I didn’t cover in this guide, consider reading theirs.
-Terfor