The Path to Greater Heights and The Crumbling Building are quests in Chapter 15, "The Day Midgar Stood Still" in Final Fantasy VII Remake, taking place at the Collapsed Sector 7 Plate. While climbing to reach the Shinra Building, Cloud Strife, Tifa Lockhart, and Barret Wallace attempt to use a building to climb further.
Nearby is a vending machine, selling the "Lurking in the Darkness" disc as well as a bench to heal up. Against upcoming enemies, Lightning Materia is useful. After resting go around to the right to find two more 3-C SOLDIER Operators and an elite helitrooper. After defeating the enemies there is a chest in the corner for 3,000 gil.
Go back to the bench to heal if needed, then use the stairs up, and stand in the spotlight to use the grappling gun. Aim up towards the ceiling and use it to reach a higher spot. Slug-Rays are fought, and can be defeated with character abilities. Head around to the left and into the spotlight, then aim up in the air to a room where Slug-Rays as well as Shock-Rays are fought, though the tactics against these are the same. Here is a chest in the corner for a hi-potion. On the opposite side of the floor and towards the right has a grapple point that will lead up. Walk around the outside down the stairs, back inside the building, and open the chest for enchanted ring. Grapple the wall opposite to get back out.
Once the Slug-Rays and Shock-Rays are defeated, use the stairs up to another floor, and then follow the path around and head outside, and a Blast-Ray is fought. This is a more durable enemy and after taking damage, is capable of using wind around it to prevent melee attacks from closing in. Use Cloud and Tifa's abilities against it first, and when it is staggered and uses its wind to push melee attackers away, if Barret Wallace is equipping a gun, he can fire against it; otherwise, it should be defeated with magic spells. Once it is defeated, climb the ladder up to the top of the tower. A turbo ether can be found here, and after this, use a ladder again to a higher floor, then follow it around to the top. Take the metal bridge path around again, and use a ladder up further onto a highway.
On the highway, move forward (south on the map) around some debris, and move forward through a linear path, to where byobapolises and cerulean drakes are fought, all of which can be defeated with spells and aerial attacks. The cerulean drakes provide an opportunity to learn Algid Aura for the Enemy Skill Materia. After dispatching the enemies, go back to find a bundle of rope on the ground. Looking up towards the scaffolding finds a grapple point that leads to a chest with a magician's bracelet. Drop down the broken ladder to proceed.
Head forward around a tower, fight another byobapolis, and proceed forward. A cutscene commences, following which the next quest, "Flight of the Valkyrie", begins.
Hard mode tips
For the first machine enemies, in the interest of conserving MP, Elemental Materia should be paired with lightning materia, rather than relying on lightning spells. As elemental materia can only be used on two characters, the third should pair it with MP Absorption Materia or HP Absorption Materia and focus on spellcasting. Cloud has the best Magic attributes, but also a strong Strength attribute and can be built either way; Tifa has the best possible physical damage output depending on her equipped weapon and can benefit from elemental materia, while Barret's ranged weapon works well with elemental materia against the Blast-Ray and allows him to preserve his low MP pool.
Against the byobapolises and cerulean drakes, Wind Materia is helpful, though pairing Ice Materia with elemental materia on armor, if the elemental materia is at max level, can allow characters to absorb ice damage and heal themselves.