Primary
You can complete this mission and kill almost no White Mantle. Simply keep hugging the left wall. With a compact group and correct timing (waiting where necessary), the White Mantle will not see you. At each tower, hug the left and you should be past (and through the gate where appropriate) before the White Mantle spread out and block the path. Since the White Mantle are in large groups, this can be a much easier way through the mission. The red path shown on the map is the shortest, but there are many others.

After collecting the scepter at point A on the map, pass through the gate and again keep hugging the left wall. Eventually, you get to a pair of towers that are teeming with White Mantle. Look carefully and you will see a boss and a narrow bridge between the towers (B on the map). Pass quickly through the White Mantle, kill the boss, and pass along the bridge to complete the mission.

Tip: If you are rushing between those two towers to the boss, make sure the boss is not blocking the path through to the bridge. If he is, fall back (pulling him from where he is) and rush again.

Bonus
You can receive the bonus objective by talking to Saidra (2 on the map) after killing the first White Mantle Seeker in a tower (1 on the map). The gate next to her will open, revealing a tower that is otherwise unreachable. Clearing the first tower (1 on the map) before talking to Saidra will not prevent you from getting the bonus.

There are nine watchtowers that each have a Watchtower Guard and a White Mantle Seeker. The Watchtower Guards can be a pain to kill, as they have Troll Unguent, but the White Mantle Seekers cannot heal, and are thus much easier to kill. Killing all nine of the seekers grants you the bonus. The text of the bonus is ambiguous, but killing the Watchtower Guards is unnecessary.

If the two White Mantle up in a tower are above the door, melee characters can attack them by standing at the door and attacking. If they move to other areas up in the tower, they will be out of reach of melee characters.

In addition to the two white mantle up in each Watchtower, each is guarded by two more that stand at its base, and a dozen or so that wander around it in several linked groups. As you approach each Watchtower, the guard will call all surrounding groups, and all the white mantle near there will come rushing to the base of the tower. The mobs up in the tower can be hard to hit, so you generally want to clear the mobs down below first. The fourth tower is also guarded by a boss, and has more mobs than normal in its vicinity.

The white mantle that guard the towers are unwilling to run very far from their spawn point, so if you pull more than you intend to, it generally isn't hard to run away. The downside of this is that if you pull only a few, they'll sometimes run away and back to the tower before you can kill them. Sometimes it is easiest to wait until mobs spread out and grab one group from that. Other times it works well to come within range of several groups and then run away until only a few stay with you.

Minions and pets won't stay where you flag henchmen, so can be overzealous about chasing mobs, and then pull more than you intended. It's easy enough to run away that this isn't a big problem, but they can still be a nuisance.

Despite the seemingly contradicting goals, this bonus and the first goal in the primary objective are both possible. You can wipe out all the White Mantle on the map and then talk to Dinas, and you will not have violated the avoid detection goal.

Tip: It may be worth working to the port, and then back to the Scepter, since that way you only need one survivor to complete the mission itself for you, in case of a wipe. Also, if you stand at the right-hand door of a watchtower, you can damage the Watchtower Guards with melee attacks.

Tip: Try to do the bonus first if you plan on doing both bonus and primary mission. The reason is that should disaster fall and you are unable to resurrect some of your party members, you can then go and speak to Dinas. The cutscene will resurrect any fallen members.

Tip: The Watchtower Guards cannot flee. Bringing indirect AOE spells like Chaos Storm, Churning Earth or Sandstorm will make very quick work of them.