Hive missions unlock after completing most of the mission chains after the end of the main campaign. I believe you have to complete all the Iconic missions, as well as another chain that opens up after those are completed. The Hive mission chain will have you complete each Hive location, ending in a 14-floor version. To get 50 clears as easily as possible, you should just repeat the power level 40 Hive mission in the Utah Badlands, as it is only 5 floors. On average it takes around 15-20 minutes to clear, though it could be as low as 10 minutes if playing with other people. Overall, this achievement will probably take about 8-11 hours.
This is also a VERY good place to work on hero levels. I believe the lowest power level you can enter the mission with is 20, so you will have to do a couple missions with each hero to reach that point. I was earning between 3-5 hero levels per run (about 10 per hour), which is very comparable, if not better than, other methods for earning hero levels, while also earning new gear and making progress to another achievement.