Engine severe damage/fire and Loss of system B
Driver 170,
I'm not B737NG rated, but I can explain you how to cope with multiple failures.
First step Engine Fire/Flameout once safety altitude has been reached.
Actions in sequence:
Memory items
Engine Fire (ENG Flameout) Emergency CKL
After T/O CKL
ONE ENG OUT abnormal CKL (Normally called out from ENG FIRE/Flameout emerg CKL)
Once all these items have been covered You'll need to enter inside the QRH looking for Relevant Inoperative Items (EICAS/EICAM will show you action still pending).
So first you'll try to close your engine chapter and only then you'll move further to Loss of HYD SYS B. This last is an abnormal situation and has less priority over an engine Fire/Flameout.
Hope it will help.
Best regards.
Markos