How to get all Graviton Cores in Final Fantasy 13-2?
In order to progress the story to the last fight with Caius. You need to get at least 5 graviton cores. There are 7 of them but 5 is required to advanced in the story. Basically after you get these graviton cores you need to bring these to Hope and Alyssa in Academia 4XX AF. On the list below is the name and location of graviton cores. First 5 of these Graviton cores are necessary to advance in the story so here it is.
Graviton Core Alpha (New Bodhum 003 AF)
Go to South from the crater, then go down to the low tide area and look for a square metal stand and then use Mog so it will reveal the Graviton Core Alpha.
Graviton Core Beta (Bresha Ruins 005 AF)
This is very tricky because the core blends with the color of the area. To get this you need a chocobo. Once you've found a chocobo and ride on it. Go back to the first gate in the area and look for a long stairs. Jump using the chocobo right beside this stair. Then unmount from the chocobo. You'll notice there will be grass and rocks. Once you see a shining crystal thing, use mog to reveal Graviton Core Beta.
Graviton Core Delta (Academia 400 AF)
Easiest way to get it is you need to go to Chocolina's location because that would be our starting point. Pass chocolina and you'll use a reverse moving escalator. Its in red, Go down there by jumping your character. Then you will see something shiny on the screen, use Mog to get this Core.
Graviton Core Epsilon (Yaschas Massif 100 AF)
This is very easy, Go to the area with spotlights. You will see on the map a large area and there's a trench in the middle of it. Once you get there, use mog to reveal the core.
Graviton Core Gamma (Oerba 200 AF)
It is required to use a chocobo to get this core. After you get one, try to find the roof with open windows at the top. Jump into that roof, unmount from the chocobo and use Mog to get Graviton Core Gamma.
Graviton Core Zeta (Oerba 400 AF)
Get this near the beach on this area. Sometimes you will see red chocobos near this graviton core.
Graviton Core Eta (Sunleth Waterscape 400 AF)
You are able to get it after getting the mini flan fragment. You will remember the location where you fight them, Its like a circle platform. You will noticed a shiny object there, that will be the graviton core eta. Use Mog to get this one. Remember to finish first the Miniflan mission before getting this core.