Primary
The idea in the first part is to sneak out and attack the siege forces from the back. Just start going east, and then south, until you reach the wall. Upon descending from the wall, keep right and then left to get back to Rurik. While approaching the mobs in front of Rurik, a group of 3 archers will come down from the left/west, which can be a great help through the rest of the mission if you keep them alive. Kill all Charr at location B on the map and get Rurik at location C on the map. Basically, you then just keep up with Rurik and help him. Try not to get overwhelmed, as there are some large mobs.

Alternatively, the first part of the mission can be done by opening the doors of the academy and keeping Rurik alive while killing the Charr that rush in. Rurik can survive if healed, and area effect spells make the Charr easier to kill. Keeping near the walls of the academy can help, as the Charr will sometimes separate into smaller groups. Not all the Charr will come into the academy, so you will still have to go out and kill some groups. Once the Charr have been beaten, meet with Rurik and follow the mission as otherwise described. This method is potentially much faster but more difficult. It also bypasses the bonus, so you will have to fight your way backwards (in relation to the path above) through part of the mission to reach it.

WARNING: Sometimes in the mission the boss right outside the Academy will not spawn when you open the doors right away, so when you kill all the Charr your quest log will still not allow you to meet with the prince. The only thing to do is restart the mission.
Rurik will first take you to the horn Stormcaller and then lead you to Rin, where you will take on successive groups of Charr, culminating in a boss.

Alternatively, it is possible to complete the mission quicker if you decide to go the opposite way that Prince Rurik goes to Stormcaller, after which you will only have to defeat a few groups of Charr and the final boss, Bonfaaz Burntfur himself, one of the Charr responsible for the Searing, and the one who managed to launch the invasion that caused the Great Northern Wall's resistance to falter. Killing Bonfaaz will trigger the mission end cut scene.

Bonus
You may commence the bonus before commencing the primary mission by exploring east (1 on the map) before opening the gate. There is a "green dot" there (Watchman Pramas), who will give you the bonus and drop the "Tome of the Fallen". Get a caster to pick this up and carry it (casters make the best carriers of items because they don't rely on melee attacks to do damage).

Continue south and head towards the wall. Go down the stairs, do not cross the gate, but continue all the way west instead. Keep left and pass west up the hill. Here it can get very nasty, especially if you have a bad group where folks rush ahead. If someone rushes ahead, you will get mobbed and the group will probably wipe. First, explore the area surrounding the Spirits of the Fallen carefully, as there are a lot of groups of hidden level 8 Devourers there. Devourers are hostile to spirits of the fallen, so a pop up group of devourers can aggro spirits of the fallen, which run around and attack. If this happens, run away and the spirits of the fallen will go kill the devourers. Once cleared, you have somewhere safe to take on the Spirits of the Fallen. The spirits of the fallen come in linked groups of three that move, and in pairs that do not move. Once they are dead, it is safe to get closer to the pedestal. Replace the tome on the pedestal, and talk to the ghost Old Ascalon Spirit (point 2 on the map). That will make the ghosts disappear and get you the bonus.

If you can, try heading up the left-hand entrance and sidle up against the wall there. Often it results in having to fight groups of only 2-3 at most.

Note: Placing the tome on the pedestal will not instantly make the ghosts disappear. Any that are already attacking your group will do so for long enough to cause serious trouble. So, make sure not to draw the attention of more ghosts when approaching the pedestal. Alternatively, have someone who has equipped a skill that allows faster movement (e.g., Sprint or Dodge) place the tome, and have them get out quickly once it's placed.

Note:Holy damage is very effective against the Spirits of the Fallen.

Note: A few pairs of the spirits will not move to attack you, even when in aggro range; they only attack if you are within melee range. Use this to your advantage and take them out with ranged attacks and spells. They will move if attacked by AoE spells but will then move back to their original location.

Note: The Devourer boss off in the Northeast corner by the cemetery can provide a recharge for Resurrection Signets. Be careful and try to lure him because several Carrion Devourers will appear when you attack.