Where to get some Accessories

Power Powder : Break a level 16 or higher Zidane.
Power Shard : Land a successful HP attack on a level 37 (Or higher) Zidane
Power Crystal : Again a successful HP attack on a level 58 or higher Zidane.
Power Orb : Break a level 100 Zidane.

Battlegen can be increased with Sunrise x2 and Moonrise x1, as well as purchasing Battlgen rate up in the PP Catalog.

Now for Gaia and Hyper Rings.

Hyper Ring - 10% Damage
Strength Powder x3
Strength Shard x2
GIL - 1000

Gaia Ring - 15% Damage
Strength Shard x3
Crimson Shard x2
Strength Crystal x2
GIL - 1800

Green Gem and Chocograph are from special code enemies.

I would advise you to just Google -

Dissidia passwords

Okay? Then from there just make sure you choose whether or not you have the US / UN / JPN Version of the game since all of their codes are different. Then once you found the right code just be sure to enter it EXACTLEY as it is into your friend card description, if you did it right you should get the friend cards.

Now from here you need to fight the enemy on the friend card, then battlegen the wanted item from them. I know for sure that the Chocograph is from the Steiner Friend Card. (You fight a Calm Lvl 100 Zidane) The green gem I'm not too sure about.

I hope I helped =P