Zero's Storyline

Yes, but don't you have to get to 180 in order to get the final one?

If I remember correctly, you can link starting from level 120. Then you get level 2 at 128 after completing the quest. Then level 3 at 138 after completing the quest. But there's no level 4. You jump from level 3 to 5 once you complete the quest at 178. (Max level is 5)

And yes, Zero levels much faster than normal characters. Though it also depends on your ability to clear the dungeons quickly.