Lockjaw is unlocked during the campaign. After completing the main story, fly up to Knowhere & into the entrance through the eye. In the back left corner is Cosmo, who you must do a fetch quest mission for. He requires 10 items that are scattered around Chronopolis. They are added to the radar, so they aren't that bad to find. One tip to save you time is there is one in Attilan, so might as well grab that one first when leaving Knowhere.
After you fetch his items, head back to Cosmo to turn in & he becomes available for purchase. I believe he is 500,000 bolts to unlock.
Afterwards, simply change your party members to Cosmo & Lockjaw and you got yourself the achievement.