To get the first of the next level, you have to defeat enough enemies. To get the second of the level you're in, you have to use the first enough times (usually 8). The fourth (and final) is different, you have to have all of the first and second of each previous level to get the level4 limit for anybody ('cept Cait Sith, since he only has two levels, and no seconds to either level, and Vincent doesn't have any seconds either).