"First boss" refers to the initial or starting supervisor or manager of a person in a work setting. They are usually the first person one answers to or is responsible for reporting to in their career. Full definition
If he was one of the last bosses I'd understand, but he's one of the very first bosses in the game! (n4g.com)
I played the very first boss battle a few dozen times until I finally beat it; the same goes for the second and especially the final boss. (148apps.com)
If you're not past the game's first boss encounter, in the garage, just stop reading this right now. (waypoint.vice.com)