Take no fire damage
Follow Haytham up the debris. Head up the ramp, go to the right then get onto the rafts to the left. Duck around the burning parts and you should have little trouble with this section. After Connor makes his jump to the far side of the brewery, turn to the right and head on through the doorway there. When the floor collapses, just keep moving forward and duck through the left-hand side of the burning debris. Turn to the right after that and make your way upwards.
Climb up the wall and back eject onto the suspended platform. Jump from there to get to the other wall and start climbing it up. At the top you will find your way out and the end of the mission.
To get full synch in this mission involves a careful movement along the path above.