Act 2 - Battle in the Icy Grip
Chapter 1 - The Dead City
Speak to High Commander Vahlen at the start of the chapter to learn of a Deadwalker blockade patrol nearby. He wants you to take them out.
Head into the western part of the Frozen Waterway to find the patrol, and take them out. Return to the Commander after to finish the quest.
The Icy Library
Speak to Sybil to learn about her desire to find the elven library. Agree to help, then proceed through the Chapter 1 story mission.
Eventually, you'll wind up in this small library upon entering the Commoner's Quarter. Bring Sybil to this location to encounter two Deadwalkers. Kill them, then loot three books from the library to finish the quest.
The Souls of the Elves
Speak to Rhelmar at the camp to learn about the elves' Soul Stones--he'd like you to gather 20. As you proceed through the rest of the chapter, keep an eye out for elf corpses. Loot 20 of these stones, and return them to Rhelmar to complete the quest.
Randval the Loner
Speak to Randval along the southern path of the Mercenary Camp--he wants to go out and scout. Let him do so, then proceed with the Chapter 1 story mission. When he returns to camp, ask him about his patrol to learn of a Deadwalker convoy.
While hunting down King Arandil IV in the Merchant's Quarter, follow the path to this isolated door in the central eastern area--there are prisoners on the other side. When you hear them call, take out the nearby Deadwalkers and head through the door. Inside, speak to the prisoners and a two more Deadwalkers will attack. Take these out, then send the prisoners on their way to end the quest.
Prerequisite: Recruit Mathras
When you return to the camp, speak to Sybil again to learn of her interactions with Mathras; she wants to no more about his sex life (no, really). Speak to him about just that, then relay the info to Sybil to finish the quest.
When you return to the camp, speak to Rhelmar again. He'd like you to craft some traps for him. Craft 10 and hand them over to finish the quest.
Help the Elf Sentinels
Prerequisite: Complete the Chapter 1 story mission
After killing King Arandil IV, you'll have to return to camp. When you pass the eastern watchtower, the sentinel will inform you that the other one has been captured, and the blockade patrol has returned. Head to the spots marked on the map and take out the Deadwalkers there to re-secure your positions and complete the quest.