Tales of Symphonia/Devil's Arms

After finding one of the Devil's Arms, talk to Abyssion in Flanoir. He is located by the boarded up building near the entrance to Flanoir. He will tell you a story and then give you Nebilim and Nebilim's Key.

The Devil's Arms
Nebilim
 * Flanoir-Given to you by Abyssion at the start of the sidequest

Evil Eye
 * Toize Valley Mine-Found by examining the remains of Naploosa Bacura

Soul Eater
 * Triet/Triet Desert-Talk to the people in Triet until you hear a story about a worm in the desert. Walk around the desert until you find a glowing ring, which will trigger a battle with the Sand Worm. You receive Soul Eater upon defeating it

Fafnir
 * Gaoracchia Forest-In a black chest

Disaster
 * Altamira-Purchase from a man outside casino on the bridge (you might have to try a few times in order to get him to sell it to you, it needs to be nighttime, and you need to have Fafnir)

Heart of Chaos
 * Flanoir/Hakenosia Peak-After every other Arm has been collected, talk to Abyssion. He will leave and Llyod will tell you that the geezer on Hakenosia Peak probably has it (note: Llyod's right)

Gates of Hell
 * Earth Temple-In a chest near the dragon. All five gnomlettes must be there before they let you pass (One is in Altessa's House)

Diablos
 * Latheon Gorge-In a black chest

Apocalypse
 * Welgaia-Found in a black chest in the large building

The Abyssion Battle
After getting every Devil's Arm, go to the Shadow Temple. At Shadow's seal (bottom level), you will find Abyssion. After a short cut scene, you will fight him. Hit him with everything you have and have a lot of recovery items (life bottles, lemon gel). Eventually, he will go down (he has 120,000 HP), and give you usage of the Devil's Arms.

Aftermath
After you win the Devil's Arms from Abyssion, you can utilize their full potency. Every enemy you defeat with an Arm will increase that Arm's attack by 1 point. In this manner, you can create immense damage with just one hit.