Flight of the Valkyrie, To the Stairs, In Hot Pursuit, and To the Top of the Plate are quests in Chapter 15, "The Day Midgar Stood Still" in Final Fantasy VII Remake. The quests take place at the Collapsed Sector 7 Plate. While climbing to reach the Shinra Building, Cloud Strife, Tifa Lockhart, and Barret Wallace encounter the Valkyrie, which fires at them to halt their progress.
Walkthrough[]
When the Valkyrie vehicle appears, hide behind cover. Wait until the Valkyrie stops firing, and run across to the next piece of cover behind the metal containers. At the end, run to the stairs and run down to a wide space, where a Blast-Ray is fought. Use character abilities to deal damage until it is staggered, then cast spells, particularly 
Lightning Materia spells, to defeat it after it uses its wind move to push characters away. Defeat it using the same tactics as before, and then proceed up a ladder. Elite helitroopers are fought here, and can be defeated using aerial attacks or spells.
Proceed forward, and a bench and vending machine can be found. Heal at the bench, run up the stairs, and obtain the antidote from the treasure chest on the left, then run down and around to the right, pick up the treasure chest from behind the stairs, and run up the next set of stairs, and a cutscene commences.
When the quest begins at the top of the tower, run over to the rope and aim the grappling to the left and above Cloud, where rope hangs from a steel beam. Run forward again to more rope, then aim the gun once again at the beam above with hanging rope. Above this, using the grappling gun again will lead to a boss battle. To prepare against it, the lightning materia and Wind Materia are both useful, especially if paired with 
Elemental Materia. Ranged attacks have a reduced effect on its stagger gauge, meaning Barret should equip a melee weapon (the 
Steel Pincers or Wrecking Ball), or be focused towards spellcasting and towards tanking damage. Because the boss is flying, Tifa and Cloud's character abilities, as well as Barret's melee abilities, struggle to reach it, meaning they should equip magic materia to use their ATB gauge.
After a short cutscene, sprint towards the camera and run left or right to avoid the Valkyrie's gunfire. Following another quick cutscene, the boss battle commences.
The Valkyrie boss[]
Fighting the Valkyrie.
The Valkyrie is a flying enemy capable of using powerful ranged attacks. Using magic spells and ranged attacks from Barret's guns lowers its attacks slowly, but aerial attacks from Barret's melee weapons, or from Tifa or Cloud, build its stagger more quickly. Most character abilities from Tifa and Cloud cannot reach it, leaving only Barret's ranged abilities. After dealing minor damage to it, a cutscene commences, and the Valkyrie is fought in a different area. Later, it can also drill into the ground and spin, making melee characters vulnerable; stay in the back until this ends.
Use aerial attacks from Cloud and Tifa and any abilities from Barret, while ensuring the party stays healed. Later on, the Valkyrie will fly a little closer to the ground, allowing Cloud and Tifa to unleash their more powerful character abilities and set up a stagger. Once a stagger is set up, use Tifa's Unbridled Strength techniques to increase the damage it takes, and lay into it with abilities and spells from all characters.
After it is reduced to a third of its HP, the Valkyrie uses Limiter Override, and all attacks against it have limited effect on stagger. Wait until it is closer to the ground, and use character abilities again to stagger it instead. Other than this, aerial attacks and spells apply just as before.
Once it is defeated, a cog bangle drops, and a cutscene commences, and the next quest, "Infiltration", in the next chapter, "The Belly of the Beast", begins.
Hard mode tips[]
Lightning materia is useful against the Blast-Rays as before, and can be paired with Elemental Materia on Barret's weapon to deal damage to it from a range without having to expend MP, and Cloud or Tifa can also benefit from it as usual. Against the helitroopers, it is equally useful to pair Fire Materia with elemental on a weapon or armor; on armor, it will absorb some of their fire attacks, and on a weapon, it will exploit their weakness. Barret can use it on a weapon to hit them reliably, while Cloud or Tifa can absorb their attacks.
Against the Valkyrie, once again, wind materia can be paired with elemental materia to great effect offensively, though pairing elemental with fire materia can absorb damage. Barret may be best pairing elemental with wind to boost ranged damage, while Cloud or Tifa use it to absorb fire damage. Cloud can pair it with HP Absorption Materia or MP Absorption Materia and focus on spellcasting in the downtime when the Valkyrie is out of reach, taking advantage of his balanced attributes. 
Steadfast Block Materia should be equipped on Cloud and Barret, though Barrier Materia can be paired with Magnify Materia to cast 
Manawall on the entire party to similar effect. Warding Materia can be paired with Binding Materia.
Early on, focus on pressuring and staggering it with Barret's guns and Focused Shot at two ATB bars. Once it is vulnerable, use Tifa's Unbridled Strength and True Strike to increase bonus damage. In its third stage, Barret should use Lifesaver with Regen cast on him, and if possible, Manawall should be cast on the party, though the same tactics apply: use spells and abilities that stagger it, then use Tifa to increase its bonus damage and lay into it while staggered.
Defeating the Valkyrie will award Barret the Sharpshooter's Companion Vol. XII.