This must be done on legendary and it can be done in co-op or single player, it depends on your preference really. It can be a mixture of both solo and co-op, (read the EDIT below)
it takes the best time from whichever you did it in whether it was in solo or co-op. Some also Have reported that the achievement did not unlock in game but at the main menu looking at their times for each mission.
This will not be easy,this will take a lot of practice and patience.
I've been informed that it can be done in one sitting or in multiple, it takes your best legendary times from all the missions combined so you can keep trying at a mission. You should do it with the time turned on to see how long you're taking on each mission.
I suggest practicing each mission before hand to get down your technique so that you know what to do and are never confused meaning go for the collectibles then this.
This Achievement was named after a person who did a speed run of the first Halo for charity. when going for this achievement you should use this video to help you. (game starts at 6:50)
It's of goatrope running through the game and his final time was 1:51:19 so there is a whole hour of error available. It's also helpful that he is commenting the entire video of what should be done.EDIT:
Using skulls that have a multiplier less than 1.00 will also void your time.
If you don't like goatrope's run through use http://www.haloruns.com/
as a guide for atticus's run through.
When attempting this in co-op make sure that everyone knows where to go and that someone is always in cover to respawn those who die.
Most of the videos on the Internet use glitches that are incredibly difficult to do so try to cut down as much time as possible on certain missions so that you can have extra time to spare on others.EDIT:
According to hypobonix "Saving and quitting will set the timer back to whatever time you were at during your most recent checkpoint. As opposed to reloading the checkpoint which keeps the timer going."EDIT:
There have been reports of some people not earning it when they have mixed there time in Co-op and Solo. If you have an issue unlocking the achievement for your mixed times is to finish all levels solo and it doesn't have to be record speed. If your finish all levels solo and then your co-op it will then mix your times together."Hybridchld"
has stated in the comments;
"For anyone having trouble getting this with mixed co-op and solo times I managed to get it mixed. What you need to do is make sure you have every level completed solo, times don't matter you can even use zero score skulls. Once you have that the game takes the best of your solo and co-op times.
This method has gotten me the speed run achievements for CEA and ODST."