The Burning Forest, Fire from Ice, and Army of the Dead are three missions as part of the Carnán storyline in Middle-earth: Shadow of War.
These unlock one after another, and come after completing A Stench on the Wind, Of Ghúls and Graugs, and The Archers of Morgoth quests earlier on.
If you are interested in completing other missions in the game, our Shadow of War guide and walkthrough can help.
The Burning Forest
Prerequisites: Complete Of Ghúls and Graugs and The Archers of Morgoth.
Reward: 22370 XP, 1080 Mirian
Purify the Necromancer Totems: You should be an expert at this by now. The bushes are ablaze, so be careful not to set yourself on fire!
Return to Carnán.
Protect Carnán from the Torchbearers: Orcs with torches will be surrounding the base of the tree. Take out as many as you can, and keep an eye out for more appearing - you'll need to hold them off for a couple of minutes before they stop sending in reinforcements. We found it quite efficient to grab a Caragor to make traversing up and down the line a quicker experience.
Meet With Carnán: Head to the marker.
Fire from Ice
Prerequisite: Complete Burning Forest.
Reward: Dragon Song skill upgrade, 23935 XP, 1100 Mirian
Reach the Ritual: Head to the middle of the lake. Hurrah, it's Zog again!
Purify Every Necromancer Totem: This is slightly complicated by Zog's presence, but if you try and keep him far away it's a little easier to manage - you can cheese it slightly by kiting everyone to one side of the lake, then sprinting back to the totems and cleansing one or two in relative safety, then repeating the process.
Defeat Zog: Again. When he's nearly dead he'll point out that he's not going to really die, at which point you'll need to have your fingers poised for a QTE.
Need more help? Our Shadow of War guide and walkthrough gives you an overview of everything you need, but if you need something in particular, we have pages on Shadow of War Fortress Sieges, how to earn Mirian in Shadow of War, a guide for how to import your Nemesis and Follower to Shadow of War, collectibles guides like how to get all Shadow of War Legendary Armour and Weapons sets, a list of Lost Artifacts and Web of Fate locations, and Ithildin Door poem solutions and Shadows of the Past, along with how to grind XP in Shadow of War to power through the tricky Shadow Wars endgame and get the true ending. Finally, there's Shadow of War's army building explained and the best skills and how to earn Skill Points.
Army of the Dead
Prerequisite: Complete Fire from Ice.
Reward: 25610 XP, 1100 Mirian
Purify the Necromancer Totems: There are four around the perimeter of the arena, one on the outer ring of the central area, and one right in the middle, and each is guarded by a random low-level Captain and a few grunts.
As before they will continue to respawn until their respective totem is down, so just eliminate enough to give yourself breathing room rather than spending too much time trying to kill them all. We'd suggest starting with the outer Totems and leaving the lower ones until last - Zog is here, and you want to avoid attracting his attention as long as possible.
Destroy Zog Once and For All: Having been dead seems to have agreed with him, and he's far tougher than in the earlier encounters. The same tactics will work, but he can take a lot more punishment and will hit you an awful lot harder, so we'd suggest keeping your distance and using ranged attacks as much as possible - kiting him around the upper ring of the Arena will provide some cover, fresh batches of Elf Arrows, and the odd rat to Drain to get some health back.
If you decide a straight up fight is preferable to giving him the runaround we'd strongly suggest still delivering the final blow with a ranged shot - finishing him off with a melee blow will trigger a QTE, and if you fumble it he'll regain half his health.