If you look across the world throughout your journey, you’ll find several special video spheres, all of which are associated with Auron’s Overdrives - get more of these to unlock more of his Overdrives. (See Auron - Bushido for more details.) Below, I will simply list where you can find most of these Auron’s/Jecht’s/Braska’s Spheres. Note that you’ll need the airship for the majority of these.
Jecht’s Sphere: Found as a part of the plot just after beating the Spherimorph.
Jecht’s Sphere: Look beside the temple in Besaid Village.
Jecht’s Sphere: Look on the main deck of the S.S. Liki.
Jecht’s Sphere: In Luca, head to towards the Auroch’s locker room. Remember, from the main hub of the area, that’s the area on the right side of the stairs at the back. The sphere is just outside.
Jecht’s Sphere: At the end of the Mi’ihen Oldroad, near where the Mars Crest chest is. You’ll have to access it from the Mi’ihen/Mushroom Rock checkpoint and go southeast from there.
Auron’s Sphere: On Mushroom Rock Road, south of the large elevator.
Jecht’s Sphere: Near the tent in the Moonflow’s South Wharf with the Save Sphere.
Jecht’s Sphere: Just run along the eastern part of the southern Thunder Plains. It’s near a lightning rod.
Jecht’s Sphere: When you enter Macalania Woods, go east from the entrance.
Braska’s Sphere: Down the thin northwestern path on the Mt. Gagazet Trail.