For the Ultimate Weapon Bracelet, you need Mysterious Parts: Alpha, Beta, and Gamma.
This is found in Mural Town. It cannot be missed.
Found in the Ancient Factory in a chest. The chest is located in the circular room with the Double Lances statues. You will pass this room during the story. The Double Lances statues are in the circular room. Approach each one until one comes to life. Defeat it, then approach statues until another one comes to life. Defeat. Rinse and repeat until all Double Lances are dead. A chest will appear that contain Mysterious Part Beta.
Found in Mecha Base High 1F. It will be in a treasure chest.
Once you have all three, go to the professor in Jibral Castle in the basement. He will make the Ultimate Weapon Bracelet.