Units were only required to maintain diaries during hostilities - these being called war diaries. Day to day occurrences were recorded on the soldiers' documents, and unfortunately most of the service records which have survived are the copies held by the Record Offices back in the UK. The documents held in the unit should have been exact duplicates but frequently the man's conduct sheets (Army forms B 1201 and B121) were not sent back to the record office on the man's termination of service.
You may be lucky and discover some paperwork relating to his District Court Martial in the National Archives, although many of these records have not yet been digitised, so that would require a personal visit to Kew. More on how to search these records here:
https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/courts-martial-desertion-british-army-17th-20th-centuries/ The 'with ignominy' sentence was generally used where the offence involved behaviour with which the Army thoroughly disapproved, so not drunkenness, fighting or absence for instance, more likely to be cowardice, 'unnatural' or lewd behaviour, or gross insubordination. That said, there are few written instructions available to indicate exactly which offences qualified for this sentence. The court would have been advised by a judge advocate who would outline the available sentencing options.
The word in his service documents before hard labour is short for "imprisonment" .