Nagato Makes Moving Easy Achievement in Halo: The Master Chief Collection

It's worth noting that you may want to grab two or three Co-Op partners when working on this achievement for two reasons. One, the extra firepower will help put down enemy forces a little quicker. Secondly, one or two players can usually act as a decent distraction while the remaining two players attempt to push on and run by as many enemies as possible in an attempt to grab the next checkpoint (on certain occasions). 

This essentially means that you may want to replay individual missions dozens of times in order to perfect your runs and learn combat tactics. Additionally, this achievement does not need to be attempted in one continuous run. Rather, the game will track your best time on each mission completed on the Legendary difficulty setting and add them up for a grand total. When a new "Personal Record" is set for that mission, it will override the previous tracked time. This means that you can tackle a mission multiple times in an attempt to perfect your speed run. 

Halo 3: ODST’s Campaign missions are generally short and aren’t too hard compared to other games in the series, so at times, even a semi-casual playthrough of the Campaign on Legendary will net this achievement without much thought or skill. Also, take note that the various segments of the New Mombasa Streets do not add time to the counter, so you can take all the time you desire exploring for audio logs and clues.