Presumably you know which Squadron the Halifax flew with; if you only have the serial number drop an email to
[email protected]
The squadron ORBs are now available online
Royal Air Force operations record books 1939-1945 | The National Archives although it can be rather expensive, as you download them a month at a time. They are free to view at Kew, and you don't need a reader's ticket to see online records there. On the other hand, you will need a ticket to see records from OTUs etc., as they have not yet been digitised.
Bomber squadron ORBs are usually relatively informative, listing the crews for each night's operations, with a brief summary of each crew's report, or - in many cases - "Failed to Return".