Walter lured Joachim by promising him eternal life with the gift of vampirism. Later, after becoming a vampire, Joachim attempted to usurp the position of his superior, but Walter's mastery of the Ebony Stone proved to make him unbeatable to Joachim and he defeated him with relative ease.
Amused by the fact that Joachim tried to defeat him, Walter decided to indulge him, and at the same time establish his own personal way of supremacy. Rather than destroying Joachim, he imprisoned him in the Dark Palace of Waterfalls, sealing one of the keys to Walter's inner sanctum with him. As Joachim's current location was blocked off by streams of water (the touch of which is like acid to a vampire and to many of Walter's own legions of monsters), Joachim could never leave. Maddened by hunger, Joachim was constantly reminded of the indignity forced upon him by Walter. He used Joachim for his own amusement, luring any adventurer who had entered his domains to confront him.
Suffice to say, when encountered by Leon Belmont as the boss of the Dark Palace of Waterfalls, Joachim had ample frustration to vent, hoping to slay Leon, drain his blood and (hopefully) gain the strength necessary to break free from his prison and exact revenge on Walter. He however is defeated by Leon.
After finishing the game as Leon, Joachim can be used as a playable character by entering "@JOACHIM" on the name entry screen. There are several major changes to the gameplay, as Joachim cannot carry healing items and is physically weaker than Leon, which increases the difficulty. These disadvantages are balanced by increased speed and powerful magic attacks. There are no cutscenes to drive the plot, save for a very brief scene after defeating the final boss (in which Joachim becomes the lord of the castle and sits on Walter's throne), although the images shown during the credits differ from Leon's ending.
It might be worth noting that Joachim is the only playable villain in the Castlevania series (aside from the Lords of Shadow saga and Castlevania Judgment), although his antagonistic nature is softened by his somewhat sympathetic portrayal in his cutscenes, as well as his unfortunate circumstances.
The name Joachim is of Hebrew origin and means "God will establish". This is probably a reference to the Crusades that took place during the year 1094 in which Lament of Innocence is set, seeing as how the main goal of the campaign was to recapture Jerusalem from the Muslims.
While playing as Joachim in Joachim Mode, it's possible to collect all of the Orbs except for the White Orb, which is not present in the room where it's found in the main game. The Black Orb, on the other hand, is still obtainable by defeating the Forgotten One, despite its uselessness.