What i did for this achievement was to play through on recruit and wait untill i'm ready for the final mission of the game. By that time you should have fully upgraded squads with terminator armour. Now you can pick any mission you have left or a timed assasination mission and just rush through.
Due to the low difficulty and the heavy armour you shouldn't be too bothered by the enemies on the way and can pretty easilly get to the mission objective(s) and only focus on them.
I Managed to push it down to just under 4 minutes without even really trying. (i used the commander to go solo to aquire a warshirne while the rest followed the above guide.
Goood Hunting! :)