This is a guide for Legendary but you can still use this information to help you with Heroic difficulty.
Halo 3: ODST is the shortest and probably easiest out of the Halo: Master Chief Collection. There are a few achievements which require completing the game on Legendary anyways so you might as well focus on them.
1) You must beat the game under 3 hours on Legendary. You probably will end up getting this by playing in coop or going through the game quickly by yourself.
2) You must also beat the game finishing one of the two LASO playlists. Once of the LASO playlists does not include the Mombasa streets as well as the Prologue and Epilogue which you must complete.
3) There is also an achievement for completing 3 playlists. Since the LASO Playlist is one of them, there is also one for completing a Legendary playlist which will count as a 2nd one. So if you wanted to, you could do the Legendary Playlist while speed running through it to make progress for multiple achievements.NOTE:
To be on the safe side and making sure this achievement unlocks, complete the Prologue, Mombasa Streets & Epilogue on Legendary difficulty.
Below is a Legendary playlist link, a Legendary speedrun playlist link & a LASO playlist link. Follow these videos if you should get stuck at a certain part.Legendary Walkthrough:https://www.youtube.com/playlist?list=PLI1zyR8U6_0_VG4B-sjR0...Legendary Speedrun:https://www.youtube.com/playlist?list=PL3bi5dIhs8VVMmjQ9RRsk...Halo 3: ODST LASO:https://www.youtube.com/playlist?list=PL3bi5dIhs8VUtitEn3gOA...