Boss Rush is the only other mode in I wanna be the guy. The name is self-explanatory; you must fight the 8 bosses of the game in one run, in whatever order you want.
To access the boss rush, one can either press "b" at the title screen, or select the option after the normal game has been beaten.
Your are teleported to a hub room that gives you warps to each of the bosses. The time and # of deaths are tracked in the upper left corner of the screen, and the best record is kept in the right.
Alternatively, you can head straight to The Guy and hold down "e", "n", and "d" to end the boss rush within seconds.