It looks like a green and black E.S. with gold highlights and a long spike on its left arm, however it is not an E.S. unit. It has no Vessel of Anima and draws its power directly from Wilhelm himself. Joshua is a completely new craft constructed by Wilhelm independent of the "relics of God". It is so thoroughly connected to Wilhelm that it can be thought of as an extension of his body. It is also the main generator of the Dämmerung, Vector Industries's headquarters.
Near the end of Episode III when Wilhelm and Joshua depart for Michtam the Dämmerung abruptly loses power and becomes dead in space. As Miyuki Itsumi and Togashi Yukihira struggle to get its backup reactor online they are shocked when their subordinates report that the ship's reactor suddenly "disappeared". Joshua appears again with Wilhelm before Zarathustra at the end of the game. When Zarathustra and Abel go out of control it merges completely with the device and with the remains of the twelve E.S. units to become the game's final boss.
Its closest analogy to Xenogears would make it the core of Deus, as both used the Zohar as an energy source.
One interesting note is that the Joshua looked white in color at the end of Episode II, but a close up reveals the white light makes it a pale green, and had several tubes connecting its right elbow to its left shoulder (possibly the Y-Data that Wilhelm and the Testaments are looking through).