you just need to complete 1 act in 1 hour, on NORMAL. its very easy when you have even plain geared buddies.
just remember - dont do anything but the main quest - dont stop for elites or monsters. the only thing your buddies will be doing is to clear the shortest route to the next checkpoint for you. and of course murder and maim whatever is in their way. talking shop is not advised if it means loss of movement, as well as goofing off. best to be prepared to sit for 2 hours straight with enough supplies.
dont do side quests at all - no matter how tempting
i picked up items as they dropped, switched out if better and dropped on the ground again - did not waste time to go to town and salvage. there is no time to run after pretty pixels when doing the speed run.
anyways, just a few 'serious' tips for a successful speed run.
also note, i did not get my achievements straight away. buddies also didnt see the achievements toasts except for act 2 & 5. it only showed up the next day after i posted in the bug report on us forums. no idea if my post influenced it at all. but it was there when i logged in the next night. so, all good