I´m stuck after killing the boss
Not sure if you got this completed but the following was given through the quick AI overview via google: when you kill the boss while its staggered, stunned or killed too fast by dmg-over-time effects during the phase transitions. It prevents the game from registering the death or triggering the next step.
I would tell you to try to kill the boss a little different way if possible. I dont know how fast you killed it if its just a glitch because of the too fast kill speed or what.