Named for DarkDEVASTAT10N who appears to hold the WR of 1:30 or so for the achievement:
Not much I can offer on the speedrun subject except to learn the tricks on easier difficulties and then try to apply them on the harder ones. Do not be afraid to abuse the hell out of the save/quit exploit. (save and quit if and when you die/botch an event, then resume at last checkpoint from the menu)
As per the other speedrun achievements, the 3 hours is merely a cumulative account for your best scores in the H3 Campaign on legendary difficulty so it doesn't have to be completed in one sitting. HOWEVER, you MUST complete the campaign in either solo OR co op completely for the achievement to unlock. It will not unlock if you have a mix of solo and co op levels completed.
A thing of note, like the Par Scores for 3 and 4, the save & quit exploit does NOT reset your time at the last checkpoint, only your score and death count.
As of 7/12/2014, some people are now able to unlock this achievement but a lot of people are still reporting problems.