Goad the bot into firing a rocket at you and then dodge it so that the rocket warps through the portal and hits GLADOS instead. Place a blue portal on the ground directly below GLADOS and then place an orange portal on a nearby wall. GLADOS also summons a rocket bot that, like before, actually works out to your advantage.
This is where the fight really begins and a countdown timer starts tickin' towards your death. Quickly step back through the portal to return to the incinerator, pick up the machine piece, and drop it into the incinerator before it closes up. Press the red switch inside the room to temporarily open up the incinerator. Warp to the stairway and enter the small room at the end of the walkway.
