Be mindful that this area will no longer be available after your fight with Egil at Agniratha. Your objective here is to reach the top where the Central Factory entrance is.
Points of interest while exploring the map: there's an elevator that takes you to the ground floor.
After you unlock the circular shaped stairs on the second floor go to the green traffic light area. Jump at the far right area to land on the spent fuel tank area you saw on the right side of the ground floor area.
The last point of interest is after you unlock the large door which takes you outside. You'll find an air vent you stand on and you'll ride the gust of air up up up until you land on a ledge. You'll find a second air vent to ride, do so. Once you land again, head to the right (facing inside, towards the Mechonis) and follow the path until you reach the end, where you'll see a downward sloping area. Slide down to the 2nd ledge (towards the left side as you look down). From this ledge you'll find a small tunnel that will take you to a secret area, the Machina Refuge. Remember to stock up on better weapons and if you want you can do more side quests for this area.
When you reach the top of this section, after a long run, you'll encounter Galdot in his suit with his memory totally erased at this moment. For this battle, you'll continuously encounter a future event in which a member of your team gets paralysed. Take care of enemies at each cover until you reach Gadolt. Eventually Gadolt thought to have destroyed you with Vanea guiding you and for the first time, it's Lady Meyneth's soul that saved everyone.
At this point, both Sword Valley and Galahad Fortress is now inaccessible.