Crimson Sphere 1:
Chapter 3, Bevelle. Events in Kilika open up events in Djose and Bevelle (even though Djose is a hot spot and Bevelle is not). Go to Bevelle first. Go back down to where Vegnagun was housed in the Bevelle underground, past the place where you fought Baralai in Chapter 2. This should trigger a scene and a Malboro will attack. Afterwards, the sphere is left lying on the ground. To watch it, board the Celsius and talk to Shinra.

Crimson Spheres 2 and 3:
Received at the end of Chapter 3 during the scenes in the Farplane Glen.

Crimson Sphere 4:
Chapter 3, Guadosalam. Go to the room with the round door. Climb up to the top ledge of the room. There is a crate that Yuna can climb to reach the ledge. Follow the path all the way to the treasure chest at the end. Open it to receive the sphere.

Crimson Sphere 5:
End of Chapter 4, Celsius. After the concert in the Thunder Plains, everyone goes back to the Celsius. Some uninvited guests are waiting. Buddy informs Yuna that LeBlanc and her boys are waiting in the engine room. See her immediately after he tells you this; do not speak to Shinra yet. LeBlanc is impatient and does not like to wait. She will come to see you if you wait too long and you will not get the sphere. Once the she hands it over, talk to Shinra.

Crimson Sphere 6:
Chapter 5, Bevelle's Via Infinito, Cloister 0. Go inside the Temple at Bevelle and go to the east side chamber. Pacce and his friends have found a teleport to the Via Infinito. At Cloister 0, after speaking to the mysterious person, pick up the sphere that he dropped.

Crimson Sphere 7:
Chapter 2, at Mushroom Rock Road. It does not matter who you gave the "Stolen Sphere: to; you will still get this Crimson Sphere. Find Nooj hanging around the door to the Den of Woe. Speak to him. Depending on who you gave the sphere to, he may be polite or rude. Afterwards, he will give you the sphere

Crimson Sphere 8:
Chapter 5, Bevelle's Via Infinito. At Cloister 20, you will fight an Aranea. After the battle, the Aranea drops the sphere. Make sure to it up.

Crimson Sphere 9:
Chapter 1, in front of the Den of Woe. Logos and Ormi are trying to find spheres to open the door. In their quick retreat, they drop this one behind.

Crimson Sphere 10:
Chapter 2, Guadosalam. After sneaking into LeBlanc's Chateau and finding the secret hallway, go to Logo's bedroom. It is sitting on his bookshelf beside his bed.