The Battle of the Pelennor Fields progression

I tried to go thematic with the heroes, however I couldn't pass the opportunity of giving my monotactics deck a heavy focus on eagles.

General gameplan: Attach Esquire of Gondor to Éowyn and Esquire of Rohan to her future husband Faramir (those attachments won't do much but they certainly are a nice touch). On round one, play any cards that generate you resources (Steward of Gondor / Treebeard / Radagast) or draw other cards, but hold back with your other resources for round two when you have a better idea of what do you have available. Equip Legolas with some weapons and build Beregond and Denethor as good defenders. Keep your fingers crossed your ally prisoners at stage 2 have a lot of hitpoints (there are many rather beefy ones in both decks for this exact reason). Get rid of the Wraith on Wings quickly, using Straight shot / Black Arrow / raw attack power. Ideally, you should have both Wraiths cleared out before you advance to stage 3. Once you are there, travel to Grond as quickly as you can, even if it should cost you a chump blocker thrown to the Witch-king, because otherwise Grond accelerates damage on Minas Tirith very quickly. By this point, Aragorn should have some willpower boosts and your eagles or ents should be ready to handle the combat. Once they are, the rest should be a piece of cake.

Notable cards - trisphere deck: At the beginning, both Merry and Faramir mostly quest, once you have enough other questing power, they can hold back for combat / Merry's threat reduction.

The allies don't need much explanation, I will only suggest to hold back your Warden of Healings every round and only heal with them after staging, protecting them from treacheries pinging every exhausted character.

The attachments once again help turning Aragorn into a superhero (Banner of Elendil, Celebrían's Stone, Ring of Barahir, Sword that was Broken) but there are also some Dúnedain signals to boost your attack (with Legolas and Faramir being great targets) and defense (Denethor is a better target because once both he and Beregond have the Gondorian Shield attached, Denethor will still need some additional boost to stand his ground against the Witch-king). Unexpected Courage first goes on Beregond and then on Legolas.

Don't hesitate to use Deep Knowledge immediately when you see it, card draw is the biggest weakness of this fellowship. Note the presence of Power of Orthanc as there are some pretty annoying conditional attachments.

Mulligan for: Steward of Gondor (which goes on Denethor who can then redistribute), Warden of Healing. Other great cards to play early are Gléowine, Deep Knowledge, Unexpected Courage or any of Aragorn's attachments.

Notable cards - monotactics deck:

This deck is basically a mixture of an eagle and an ent deck. Radagast and Treebeard are your resource acceleration (although the occasional resource from Denthor passed onto Beregond doesn't hurt). Your other important ally is Eagles of the Misty Mountains that can help Beregond defend and Legolas kill basically anything once boosted by enough other eagles in combination with Support of the Eagles. Don't hesitate to assign the occasional direct damage to your ents, boosting the Booming Ents.

Rivendell Blade on Legolas enables you to quickly get rid of a Mumak through Straight Shot (alternately you can use two blades to use the same event on a Wraith). Gondorian Shield boosts first Beregond and then the second copy goes on Denethor. Daggers of Westernesse are great on Faramir or Aragorn.

Mulligan for: nothing is really The Card to mulligan for, but your key cards are Gondorian Shield, Treebeard, Radagast, Rivendell Blade, Eagles of the Misty Mountains and Foe-hammer.

This quest is obviously one of the more difficult ones so don't expect to always win - but if you enter stage three with a reasonably established board state, you have a fighting chance.